21. Topology - Wikibooks, Collection Of Open-content Textbooks General topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, http://en.wikibooks.org/wiki/Topology

Topology From Wikibooks, the open-content textbooks collection Jump to: navigation search Contents Introduction Before You Begin Point - Set Topology Some Set Theory ... edit Introduction General Topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, though this will not be immediately apparent for the novice student. Topology generalises many distance related concepts, such as continuity, compactness and convergence. For an overview of the subject of topology, please see the Wikipedia entry edit Before You Begin In order to make things easier for you as a reader, as well as for the writers, you will be expected to be familiar with a few topics before beginning. (I hope to have some links to other Wikibooks here soon.) Real analysis Continuous Functions Set Theory Set Operations: Union, Intersection, Complement, De Morgan's laws , etc. Order Relations : Ordered Sets, Equivalence relations, Lattices Functions: Definition and Properties of Functions Cardinality : Finite, Countable, and Uncountable sets

22. What Is Topology? topology is a branch of mathematics. It studies the properties of objects that do not change when the object is distorted. In topology two objects are http://www.questacon.edu.au/html/what_is_topology_.html

What is Topology? Questacon Teachers Outreach Programmes Tenix Questacon Maths Squad ... Post Visit Activities Tenix Questacon Maths Squad Topology Maths Squad Activities What is Topology? The Handcuffs Puzzle Handcuff Puzzle Images Möbius Strip ... Bubble Mix Recipe In some of these activities you will find references to topology. Topology is a branch of mathematics. It studies the properties of objects that do not change when the object is distorted. In topology two objects are considered to be the same if each one can be distorted to the other without being cut or torn. There are everyday examples of topology. A typical map of a railway system shows the railway lines and how they connect in very simple form. An accurate map of a railway system would have lots of bends and uneven spacing. The simplified map is topologically equivalent to an accurate map. The important information, like the order of stops and how the different train lines are connected, does not change as the map is distorted from one to the other. There are three topological activities described here. The first is the

23. Topology Web Site The research community, however, has not seen many systematic empirical studies of how the Internet topology evolves over time and in space. http://topology.eecs.umich.edu/

Topology Project The exponential growth of the number of Internet hosts has been well documented in the trade press. The research community, however, has not seen many systematic empirical studies of how the Internet topology evolves over time and in space. Most recently, the authors of [FFF99] report on several power-law relationships observed on Autonomous Systems' (AS) connectivity degree, degree frequencies, and the neighborhood size within any given hop count from an AS. This pioneering work represents a first important step toward a better understanding of the dynamic nature of Internet topology, a topic we explore further in this project. PIs: Ramesh Govindan Sugih Jamin Scott Shenker Walter Willinger Students: Hyunseok Chang Cheng Jin Hongsuda Tangmunarunkit Jared Winick ... Inter-AS Traffic Demand Model Data Sets Papers: To Peer or not to Peer: Modeling the Evolution of the Internet's AS-level Topology in Proc. of IEEE Infocom, 2006. An Empirical Approach to Modeling Inter-AS Traffic Matrices in Proc. of ACM Internet Measurement Conference, 2005. Towards Capturing Representative AS-Level Internet Topologies Computer Networks Journal, Volume 44, Issue 6, pp 737-755, April, 2004.

24. British Topology Home Page A source of pointers to topologyrelated sites, including archives and conference announcements. http://www.maths.gla.ac.uk/~ajb/btop.html

Number of non-local hits since 26 August 1997 The British Topology Home Page Rotating Immortality - a Möbius Band in the form of a Trefoil Knot by John Robinson with graphics by Ronnie Brown and Cara Quinton. Borrowed from `Symbolic Sculptures and Mathematics' This site is intended to act as a convenient source of pointers to Topology-related sites, including archives and conference announcements. It is not intended to be part of a British archive as such, but pointers to useful sites will be included to form a `nonlocalised' archive. Although intended mainly for British and general European use, it will include references to other parts of the world. To have items included, either email them to me or (preferably) send addresses of existing web documents. Conference notices and other items with a finite lifetime will normally be removed when the advertised events have occurred. Please let me know of any errors or links that you would like to see included. I would be grateful for comments on the structure and contents of this site. Anyone wishing to set up and maintain a subsidiary page of this site is encouraged to do so. Andrew Baker email Topologists' Home Pages - includes the Database of Topologists Topology Photo Gallery Topology groups Topology seminars and other regular activities ... Conferences and meetings on Topology and related topics This is now maintained by Sarah Whitehouse to whom all items for inclusion should be sent Topology resources Past and future British Topology Meetings Some comments by Frank Adams

25. Chapter 5: Topology Common physical topologies for computer networks are introduced. The advantages and disadvantages of the linear bus, star, starwired ring, http://fcit.usf.edu/network/chap5/chap5.htm

What is a Topology? The physical topology of a network refers to the configuration of cables, computers, and other peripherals. Physical topology should not be confused with logical topology which is the method used to pass information between workstations. Logical topology was discussed in the Protocol chapter . Main Types of Physical Topologies The following sections discuss the physical topologies used in networks and other related topics. Linear Bus Star Star-Wired Ring Tree ... Summary Chart Linear Bus A linear bus topology consists of a main run of cable with a terminator at each end (See fig. 1). All nodes (file server, workstations, and peripherals) are connected to the linear cable. Ethernet and LocalTalk networks use a linear bus topology. Fig. 1. Linear Bus topology Advantages of a Linear Bus Topology Easy to connect a computer or peripheral to a linear bus. Requires less cable length than a star topology. Disadvantages of a Linear Bus Topology Entire network shuts down if there is a break in the main cable. Terminators are required at both ends of the backbone cable.

26. Topology Proceedings topology PROCEEDINGS publishes two issues each year. Issue No. 1 contains the proceedings of the Spring topology and Dynamics Conference and it is published http://topology.auburn.edu/tp/

27. ALGTOP-L, Algebraic Topology Listserv The primary functions of this list are providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, http://www.lehigh.edu/~dmd1/algtop.html

ALGTOP-L, Algebraic Topology listserv This listserv began as a discussion group in July 1995, and was converted to an automated moderated listserv in Sept 2007. To join the listserv go to https://lists.lehigh.edu/mailman/listinfo/algtop-l The primary functions of this listserv are providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology. This website also serves as an archive of links to websites related to algebraic topology. The Hopf archive is a preprint server for papers in algebraic topology. It is maintained by Clarence Wilkerson. Once a month, Mark Hovey posts abstracts of papers which have been added to the Hopf archive. Information about conferences Messages posted to the Discussion Group 1998-Sept. 2007 . The postings to the listserv are archived on the listserv. Anyone, including nonmembers, can read them here To obtain a list of our subscribers' e-mail addresses, you must now join the listserv, where this information is readily available. Links to home pages of algebraic topologists,

28. Topologies - Network Topologies - Types Of Topology Examples - Bus Ring Star Common network topologies include the bus topology, star, and ring. Learn more about these and other topologies in computer network design. http://compnetworking.about.com/od/networkdesign/a/topologies.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') You are here: About Wireless / Networking Networking Basics Topologies - Network Topologies - Types of Topology Examples - Bus Ring Star Wireless / Networking Wireless / Networking Essentials Wireless Router / Broadband Networking ... Submit to Digg Suggested Reading Introduction to Area Networks Network Bandwidth and Latency Network Topology - Related Topics The OSI Model Network Protocols Recent Discussions Geolocation Question acess point College Student: Networking Most Popular Limewire Free Client Downloads Find IP Addresses of a Router Free P2P File Sharing Software Network Topologies From Bradley Mitchell Your Guide to Wireless / Networking FREE Newsletter. Sign Up Now! Bus, ring, star, and other types of network topology In networking, the term "topology" refers to the layout of connected devices on a network. This article introduces the standard topologies of computer networking. Topology in Network Design One can think of a topology as a network's virtual shape or structure. This shape does not necessarily correspond to the actual physical layout of the devices on the network. For example, the computers on a home LAN may be arranged in a circle in a family room, but it would be highly unlikely to find an actual ring topology there.

29. Topology And Geometry A collection of educational, graphical and research software by Jeff Weeks. http://www.geometrygames.org/

Jeff Weeks’ Topology and Geometry Software Torus Games Eight familiar games introduce children age 10 and up to the concept of a finite yet unbounded universe. Mac OS X Windows XP info download Kali Children of all ages create beautiful art based on the 17 tiling patterns. Windows 95/XP , Mac Classic info download KaleidoTile Explore polyhedra and tessellations while creating colorful works of art. Windows 95/XP , Mac Classic info download Curved Spaces Math and physics students experience flight in a multiconnected universe. Mac OS X Windows XP info download Exploring the Shape of Space Two-week geometry unit introduces students grades 6-10 to multiconnected universes. info download SnapPea Researchers create and study 3-manifolds. Mac OS X , Linux, Mac Classic info download Recent Updates SnapPea Link editor modified to accommodate 12" MacBooks SnapPea SnapPea for Mac OS X, development release 00 Kali Swedish added, thanks to sa Kronkvist

30. Topology vls.icm.edu.pl/cgibin/sciserv. pl?collection=elsevier journal=00409383 - Similar pages Journal of topologyIt is with great pleasure that we announce the launch of a new journal, to be called the Journal of topology, that will publish its first issue in January http://vls.icm.edu.pl/cgi-bin/sciserv.pl?collection=elsevier&journal=00409383

31. Oxford Journals | Mathematics & Physical Sciences | Journal Of Topology The Journal of topology publishes papers of high quality and significance The Journal of topology will appear in quarterly issues with articles posted http://jtopol.oxfordjournals.org/

@import "/resource/css/main.css"; @import "/resource/css/homepage.css"; @import "/resource/css/journal.css"; @import "/resource/css/jtopol.css"; @import "/resource/css/progress.css"; Skip Navigation Oxford Journals Contact Us My Basket ... My Account Journal of Topology About This Journal Contact This Journal Subscriptions Current Issue ... Oxford Journals Journal of Topology Read This Journal View Current Issue (Volume 1 Issue 1 January 2008) Advance Access Browse the Archive New to Oxford Journals in 2008 - free access The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology will appear in quarterly issues with articles posted individually online, and will be made freely available online in its first year. Search This Journal Advanced search Related Journals Bulletin of the London Mathematical Society Journal of the London Mathematical Society Proceedings of the London Mathematical Society The Quarterly Journal of Mathematics Reader Services Read volume 1 free online Subscribe to the Journal of Topology The Journal About the journal Dispatch date of the next issue Editorial Board View full editorial board Published on behalf of

32. Geometry & Topology Outdated Archival Version. These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, http://www.emis.de/journals/GT//index.html

Outdated Archival Version These pages are not updated anymore. They reflect the state of 21 Apr 2006 . For the current production of this journal, please refer to http://msp.warwick.ac.uk/

33. 54: General Topology topology is the study of sets on which one has a notion of closeness enough to decide which functions defined on it are continuous. http://www.math.niu.edu/~rusin/known-math/index/54-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 54: General topology Introduction More formally, a topological space is a set X on which we have a topology a collection of subsets of X which we call the "open" subsets of X. The only requirements are that both X itself and the empty subset must be among the open sets, that all unions of open sets are open, and that the intersection of two open sets be open. This definition is arranged to meet the intent of the opening paragraph. However, stated in this generality, topological spaces can be quite bizarre; for example, in most other disciplines of mathematics, the only topologies on finite sets are the discrete topologies (all subsets are open), but the definition permits many others. Thus a general theme in topology is to test the extent to which the axioms force the kind of structure one expects to use and then, as appropriate, introduce other axioms so as to better match the intended application. For example, a single point need not be a closed set in a topology. Does this seem "inappropriate"? Then perhaps you are envisioning a special kind of topological space, say a a metric space. This alone still need not imply the space looks enough like the shapes you may have seen in a textbook; if you really prefer to understand those shapes, you need to add the axioms of a manifold, perhaps. Many such levels of generality are possible.

34. Nsf.gov - Mathematical Sciences (DMS) Funding - Topology - US Supports research on algebraic topology, including homotopy theory, ordinary and extraordinary homology and cohomology, cobordism theory, and Ktheory; http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=5551&org=DMS

35. Front: Math.GT Geometric Topology Preprints in geometric topology in the Arxiv. http://front.math.ucdavis.edu/math.GT

Front for the arXiv Thu, 24 Jan 2008 Front math GT search register submit journals ... iFAQ math.GT Geometric Topology Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 24 Jan arXiv:0801.3647 All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron. Cherry Kearton , Vitaliy Kurlin math.GT 24 Jan arXiv:0801.3475 Climbing a Legendrian mountain range without Stabilization. Douglas J. LaFountain , William W. Menasco math.GT math.SG 22 Jan arXiv:0801.3253 On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams. B. Bischof , R. Kogan , D. N. Yetter math.GT math.QA 22 Jan arXiv:0801.3227 A New Perspective for an Existing Homology Theory of Links Embedded in I-Bundles. Jeffrey Boerner math.GT 22 Jan arXiv:0801.3139 Existence of broken Lefschetz fibrations. R. Inanc Baykur math.GT math.SG 22 Jan arXiv:0801.3107 Approximation by light maps and parametric Lelek maps. Taras Banakh , Vesko Valov math.GT math.GN 22 Jan arXiv:0801.3058 Connectivity of the space of ending laminations. Christopher J.

36. Topology : Network : GÉANT2 GÉANT2 topology. The GEANT2 network, shown below, connects 34 countries through 30 GÉANT2 topology (map only). Network design for GÉANT2 has focused on http://www.geant2.net/server/show/conWebDoc.1144

search [advanced search] sitemap contact Topology ... Print this page The GEANT2 network, shown below, connects 34 countries through 30 national research and education networks (NRENs). All of the network's 25 Points of Presence (PoPs) are fully equipped and in service. 43 of the network's total of 44 routes are fully installed and operational, with just one of the 18 dark fibre routes still in preparation. The first links came into service in early December 2005, between Switzerland and Italy, and Switzerland and Germany, respectively. Multiple 10Gbps wavelengths are being employed in the network's core. ALICE Global Connectivity DANTE Web Archive LOGIN HERE username password [email my password] Project partners: register here See Also [pdf] Glossary FIRST Forum of Incident Response and Security Teams IP Internet Protocol NREN National Research and Education Network PoP Point of Presence About This Site Credits Legal Contact ... top of page

37. AMS Online Books/COLL27 Algebraic topology text published by the American Mathematical Society (AMS), and available as a free download in PDF format. http://www.ams.org/online_bks/coll27/

Title List Help AMS Home AMS Bookstore Algebraic Topology by Solomon Lefschetz Publication Date: 1942 Number of Pages: 389 pp. Publisher: AMS ISBN: 0-8218-3397-9 COLL/27.E Download Individual Chapters FREE (10 files - 41.5mb) Frontmatter Title Contents Preface Introduction to General Topology Additive Groups Complexes Complexes: Products. Transformations. Subdivisions ... Endmatter Appendices Bibliography and Indexes Comments: webmaster@ams.org Privacy Statement Search the AMS

38. Links To Low-dimensional Topology Topics General, Conferences, Pages of Links, Knot Theory, 3manifolds, Journals. http://www.math.unl.edu/~mbrittenham2/ldt/ldt.html

Links to low-dimensional topology Any comments/suggestions? Send them to me! Enter your comments here: Most recent additions: hard to say, I've stopped keeping track... This page was getting just a little too large, so I've cut it into pieces. General Conferences Pages of Links Knot Theory ... Home pages

39. The Network Simulator Ns-2: Topology Generation topology generation is required for network simulations. In NS2 you may create a topology for simulation using one of the following methods http://www.isi.edu/nsnam/ns/ns-topogen.html

The Network Simulator ns-2: Topology Generation Topology generation is required for network simulations. In NS-2 you may create a topology for simulation using one of the following methods: by using the Inet topology generator. by using the GT-ITM topology generator. by using the Tiers topology generator. by using the other topology generators. by hand Inet Topology Generator Generating graphs from Inet topology generator Download the Inet Topology Generator from University of Michigan and create a internet topology using the configuration parameter. Conversion of Inet output to ns-2 format Use to convert the inet topology to ns. The command to execute the script is: inet2ns ns.topology Georgia Tech Internetwork Topology Models Generating graphs from GT-ITM topology generator. Download the GT-ITM Topology Generator software. The GT-ITM topology generator can be used to create flat random graphs and two types of hierarchical graphs, the N-level and transit-stub. Take a look at the examples in Daniel Zappala's homepage . Also look at the documents under docs subdirectory of GT-ITM's distribution. For example, we need to create a transit-stub graph with 200 nodes. So we create a specification file, say ts200, that goes like this:

40. CAIDA : Analysis : Topology : As_core_network The graph reflects 926201 IP addresses and 2000796 IP links (immediately adjacent addresses in a traceroutelike path) of topology data gathered from 22 http://www.caida.org/analysis/topology/as_core_network/

HOME RESEARCH DATA TOOLS ... search: Visualizing Internet Topology at a Macroscopic Scale When the Internet was in its infancy, monitoring traffic was relatively simple. However, after experiencing phenomonal growth in the 1990's, tracking connectivity has become a daunting task. Recently, CAIDA researchers have attempted to strip away lesser connected autonomous systems (or `ASes') in order to find out how Internet connectivity is distributed among ISPs. About current AS Internet graph Available posters Previous versions IPv6 version Visualizing the AS Core We describe a visualization that shows a macroscopic snapshot of the Internet for two weeks: 4 April 2005 - 17 April 2005. Input Data The graph reflects 926,201 IP addresses and 2,000,796 IP links (immediately adjacent addresses in a traceroute-like path) of topology data gathered from 22 monitors probing approximately 865,000 destinations spread across 77,678 (50% of the total) globally routable network prefixes. We then aggregate this view of the network into a topology of Autonomous Systems (ASes), each of which approximately maps to an Internet Service Provider (ISP). We map each IP address to the AS responsible for routing it, i.e., the origin (end-of-path) AS for the best match IP prefix of this address in Border Gateway Protocol (BGP) routing tables. We use the largest publicly available set of core BGP routing tables, which are collected by the University of Oregon's RouteViews project . The abstracted graph consists of 12,979 Autonomous System (AS) nodes and 35,589 peering sessions. For 2,752 ASes we could not determine a geographical location. The resulting graph contains 10,131 AS and 29,191 peering sessions.

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