1. General Topology - Wikipedia, The Free Encyclopedia In mathematics, general topology or pointset topology is the branch of topology which studies properties of topological spaces and structures defined on http://en.wikipedia.org/wiki/General_topology

General topology From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them. It is distinct from other branches of topology in that the topological spaces may be very general, and do not have to be at all similar to manifolds Contents History Scope See also References ... edit History General topology grew out of a number of areas, most importantly the following: the detailed study of subsets of the real line (once known as the topology of point sets , this usage is now obsolete) the introduction of the manifold concept the study of metric spaces , esp. normed linear spaces , in the early days of functional analysis General topology assumed its present form around 1940. It captures, one might say, almost everything in the intuition of continuity , in a technically adequate form that can be applied in any area of mathematics. edit Scope More specifically, it is in general topology that basic notions are defined and theorems about them proved. This includes the following: open and closed sets interior and closure neighbourhood and closeness compactness and connectedness continuous functions convergence of sequences nets , and filters separation axioms countability axiom Other more advanced notions also appear, but are usually related directly to these fundamental concepts, without reference to other branches of mathematics.

2. 54: General Topology Thus a general theme in topology is to test the extent to which the axioms . Until 1958 an additional classification 56.0X was used for general topology. 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.

3. Front: Math.GN General Topology Preprints in general topology. http://front.math.ucdavis.edu/math.GN

Front for the arXiv Fri, 14 Mar 2008 Front math GN search register submit journals ... iFAQ math.GN General Topology Calendar Search Atom feed Authors: AB CDE FGH IJK ... U-Z Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 14 Mar arXiv:0803.1947 SPM Bulletin 24. Boaz Tsaban (ed. ). math.GN math.CO math.LO 10 Mar arXiv:0803.1175 Pre-Hausdorff Spaces. Jay Stine , M. V. Mielke math.GN 10 Mar arXiv:0803.1139 A short proof of nonhomogeneity of the pseudo-circle. Krystyna Kuperberg (Auburn University), Kevin Gammon (Auburn University). math.GN 3 Mar arXiv:0802.4436 Krasinkiewicz spaces and parametric Krasinkiewicz maps. Eiichi Matsuhashi , Vesko Valov math.GN math.GT 3 Mar arXiv:0802.4304 Group Actions and Covering Maps in the Uniform Category. N. Brodskiy , J. Dydak , B. Labuz , A. Mitra math.GN math.MG Cross-listings 11 Mar arXiv:0803.1387 Quasi-Minimal, Pseudo-Minimal Systems and Dense Orbits. Christian Pries , Silas Matel math.DS math.GN 6 Mar arXiv:0803.0676 Michał Machura , Katarzyna Osiak math.AC math.GN 4 Mar arXiv:0803.0219 The order completion method for systems of nonlinear PDEs revisited. J. H.

4. General Topology Authors/titles Recent Submissions Subjects general topology (math.GN); Group Theory (math.GR) Subjects Mathematical Physics (mathph); general topology (math.GN) http://arxiv.org/list/math.GN/recent

arXiv.org math math.GN Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages General Topology Authors and titles for recent submissions Fri, 14 Mar 2008 Tue, 11 Mar 2008 Mon, 10 Mar 2008 Thu, 6 Mar 2008 ... Tue, 4 Mar 2008 [ total of 6 entries: [ showing up to 25 entries per page: fewer more Fri, 14 Mar 2008 arXiv:0803.1947 ps pdf other Title: SPM Bulletin 24 Authors: Boaz Tsaban (ed.) Subjects: General Topology (math.GN) ; Combinatorics (math.CO); Logic (math.LO) Tue, 11 Mar 2008 arXiv:0803.1387 (cross-list from math.DS) [ ps pdf other Title: Quasi-Minimal, Pseudo-Minimal Systems and Dense Orbits Authors: Christian Pries Silas Matel Comments: 24 pages, 1 figures Subjects: Dynamical Systems (math.DS) ; General Topology (math.GN) Mon, 10 Mar 2008 arXiv:0803.1175 ps pdf other Title: Pre-Hausdorff Spaces Authors: Jay Stine M.V. Mielke Comments: 10 pages Subjects: General Topology (math.GN) arXiv:0803.1139 ps pdf other Title: A short proof of nonhomogeneity of the pseudo-circle Authors: Krystyna Kuperberg (Auburn University), Kevin Gammon (Auburn University) Comments: 3 pages, a short proof of an old result

5. Applied General Topology Abstracts of all volumes. http://www.upv.es/agt/

Editors-in-Chief: Salvador Romaguera , Manuel Sanchis ISSN: 1576-9402 Editorial Board Aims and Scope Technical Editors Instructions for Authors Abstracts: Volume 1, no.1 Volume 2, no.1 Volume 2, no.2 Volume 3, no.1 ... 8, no.2

6. General Topology - NoiseFactory Science Archives (http://noisefactory.co.uk) Standard notations for the basic number sets of mathematics. http://noisefactory.co.uk/maths/topology.html

This site makes extensive use of JavaScript. Please make sure JavaScript is re-enabled, and then reload the page. Sorry for the inconvenience. [See also: The Stone-Cech Compactification General mathematics Standard sets Functions ... Ordinal topologies (summary table) General mathematics Standard sets We use standard notations for the basic number sets of mathematics: R , the real line; C , the complex plane; Q , the set of rational quotients; and Z , the set of integers. We consider to be a member of N , the set of non-negative integers. The unit interval [0,1] R will be denoted I . We write to denote the empty set. Given any set X, the set of subsets of X, its power set , is denoted X or 2 X Functions Given any sets X and Y, we write Y X to denote the set of all functions from X to Y (note the reversal of the intuitive order of X and Y), and if Y is computable we can write [X Y] for the subset of Y X comprising computable functions. For the purposes of this document, we are careful to distinguish set inclusion (which allows the possibility of set equality), and strict inclusion

7. Algebraic General Topology And Math Synthesis - Replacement Of Mathematical Anal Announce of my math discoveries Algebraic general topology and Math Synthesis which replace former general topology, Math Analisys and Functional Analisys. http://www.mathematics21.org/algebraic-general-topology.html

My homepage My math page My math news Donate for the research Algebraic General Topology and Math Synthesis I discovered Algebraic General Topology AGT ), a new field of math which will replace old General Topology. Mathematical Synthesis is how I call Algebraic General Topology applied to study of Mathematical Analysis. Please nominate me for Abel Prize. AGT articles Funcoids and Reloids (PDF, draft) Consider generalizations of proximity spaces and uniform spaces. Generalized Continuousness (PDF, draft) Defines continuousness algebraically hiding old epsilon-delta notion under a smart algebra. Generalizes continuousness, uniform continuousness, and proximity-continuousness in one formula. Connectedness of funcoids and reloids (PDF, draft) Defined the notion of connectedness for funcoids and reloids. Shown how connectedness of funcoids is related with connectedness of reloids. Convergence of funcoids (PDF, draft) Defined the notion of convergence and limit for funcoids. Open Problems in AGT (PDF) This document lists all yet unsolved problems and conjectures in the field of AGT . You can discuss these open problems in Open Problem Garden and in Algebraic General Topology Research forum . If you solved any of these problems

8. Intute: Science, Engineering And Technology - Browse Topology These chapters cover the following general topology, additive groups, complexes, manifolds, topology of polyhedra, and homology theory. http://www.intute.ac.uk/sciences/cgi-bin/browse.pl?id=25620

9. Questions And Answers In General Topology Questions and Answers in general topology (abbreviation Q A) is an international journal devoted primarily to rapid publication of questions and answers http://at.yorku.ca/e/a/j/j/08.htm

Topology Atlas Document # eajj-08 Questions and Answers in General Topology A Journal Devoted to General Topology and Related Fields ISSN : 0918-4732 Commenced publication 1983. Two issues per volume, one volume per year. Published by Symposium of General Topology Audience Topologists working in general topology and related areas. Aims and Scope Questions and Answers in General Topology (abbreviation ) is an international journal devoted primarily to rapid publication of questions and answers that arise from research in general topology and related areas. Ordering Information Subscription price per year (one volume of two issues): US$60.00, or 6000 yen, in Japan. Please, send your order and cashier's check to the managing editor, Prof. Jun-iti Nagata, at the address below. Personal checks from North American subscribers are acceptable. Editorial Boad Managing Editor J. Nagata Advisors M. Atsuji, T. Ishii, Y. Katuta, R. Nakagawa, A. Okuyama, S. Sakai, T. Tanaka Editors N. Aoki, T. Hoshina, T. Mizokami, T. Nogura, Y. Tanaka, Y.Yasui Associate Editors Y. Hattori, H. Kato, N. Kemoto, A. Koyama, H. Ohta, K. Tamano, H. Tanaka, J. Terasawa, K. Yamada

10. Encyclopedia Of General Topology - Elsevier This book is designed for the reader who wants to get a general view of the terminology of general topology with minimal time and effort. http://www.elsevier.com/wps/product/cws_home/672859

Home Site map Elsevier websites Alerts ... Encyclopedia of General Topology Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view ENCYCLOPEDIA OF GENERAL TOPOLOGY To order this title, and for more information, click here By K.P. Hart , Delft University of Technology, Faculty of Information, Technology and Systems, The Netherlands Jun-iti Nagata , Uzumasa, Osaka, Japan J.E. Vaughan , University of North Carolina, Department of Mathematics, Greensboro, NC, USA Description This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: Audience Working mathematicians and graduate students in mathematics. Mathematicians working in General Topology and related areas.

11. General Topology Gudunov /Abstract, We describe a numerical technique for solving 2dimensional compressible multimaterial problems using a general topology mesh....... http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=5934854

12. Fairisle: A General Topology ATM LAN A research project investigating the architecture and management algorithms for a general topology. http://www.cl.cam.ac.uk/research/srg/fairpap.html

Fairisle: A General Topology ATM LAN Ian Leslie and Derek McAuley December 1990 An experimental general topology local area network based on Asynchronous Transfer Mode (ATM) is described. This network is intended to be used to support multiservice traffic. The provision of guarantees of quality of service to various traffic types is an important feature of the network. The management algorithms which will be used to provide these guarantees are the subject of current research; the network components described here can be viewed as a platform on which these algorithms will be developed. Fairisle is supported by the SERC under Grant GR/F 6090.8 and by HP Laboratories Bristol. Introduction Fairisle is a research project investigating the architecture and management algorithms for a general topology ATM network which is to be used as a private or local area network. Fairisle was begun in October 1989. It arose from work in the Computer Laboratory in ATM networks, multimedia communications, protocol architectures and fast packet switching. The overall purpose of Fairisle is to investigate networks rather than switches. Such an investigation is as much concerned with how components fit together as it is with network components themselves.

13. General Topology -- Britannica Online Encyclopedia No results were returned. Please consider rephrasing your query. For additional help, please review Search Tips. Search Britannica for general topology http://www.britannica.com/eb/topic-228667/general-topology

Already a member? LOGIN Encyclopædia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to this Topic Shopping New! Britannica Book of the Year The Ultimate Review of 2007. 2007 Britannica Encyclopedia Set (32-Volume Set) Revised, updated, and still unrivaled. New! Britannica 2008 Ultimate DVD/CD-ROM The world's premier software reference source. general topology A selection of articles discussing this topic. major reference Basic concepts of general topology Leibniz ...in mathematics: In March 1679 he perfected the binary system of numeration (i.e., using two as a base), and at the end of the same year he proposed the basis for analysis situs, now known as general topology, a branch of mathematics that deals with selected properties of collections of related physical or abstract elements. He was also working on his dynamics and his philosophy, which... No results were returned. Please consider rephrasing your query. For additional help, please review Search Tips Search Britannica for general topology About Us Legal Notices ... Test Prep Other Britannica sites: Australia France India Korea ... Britannica Mobile - iPhone Edition

14. Probability Tutorials: Books In General Topology R. Engelking, general topology. J.R., Munkres, Topology. J.A., Seebach, Counterexamples in Topology. L.A., Steen, Counterexamples in Topology http://www.probability.net/topology.html

www.probability.net Probability Tutorials General Topology Books A B C D ... W Contents M.A. Armstrong Basic Topology G. Choquet Topology J. Dixmier General Topology R. Engelking General Topology J.R. Munkres Topology J.A. Seebach Counterexamples in Topology L.A. Steen Counterexamples in Topology Tutorials Introduction Definitions Theorems ... Finance s="na";c="na";j="na";f=""+escape(document.referrer)

15. DEPARTMENT OF GENERAL TOPOLOGY AND GEOMETRY Department of general topology and Geometry. Members, research interests, and seminars. http://www.math.msu.su/department/gentopol/gentopol.html

DEPARTMENT OF GENERAL TOPOLOGY AND GEOMETRY BRIEF HISTORY PRINCIPAL RESEARCH TOPICS STAFF LIST COMPULSORY AND SPECIAL COURSES ... INTERNATIONAL TOPOLOGICAL CONFERENCE DEDICATED TO P.S.ALEXANDROFF'S 100TH BIRTHDAY (Moscow, May 27-31, 1996) MAILING ADDRESS: Department of General Topology and Geometry Faculty of Mechanics and Mathematics Moscow State University Vorobyovy Gory, Moscow 119899 Russia PHONE: FAX: (attn: V.V.Fedorchuk) E-MAIL ADDRESSES We refer those who would like to know more about current events in Topology around the World, to: TOPOLOGY ATLAS TOPOLOGY E-PRINTS Maintained by Andrew N. Yakivchik Please send your comments and suggestions to: anyak@nw.math.msu.su

16. SUMTOPO - The Summer Conference In Topology & Applications An annual event bringing together an international audience of researchers in general topology and related fields. Details of past and future meetings. http://sumtopo.home.att.net/

17. Pearson - Introduction To General Topology An Introduction to general topology is a clear, well motivated, rigorous introduction to pointset topology. Through careful exposition, it helps students http://www.pearsonhighered.com/academic/product/0,3110,0201756110,00.html

/*********************************************** * Tab Content script- © Dynamic Drive DHTML code library (www.dynamicdrive.com) * This notice MUST stay intact for legal use * Visit Dynamic Drive at http://www.dynamicdrive.com/ for full source code ***********************************************/ About Pearson Higher Education Find a product: Go to a discipline or Anthropology Art English History ... Exam copy bookbag Addison-Wesley / Prentice Hall Mathematics Browse available resources for Mathematics: Select a resource Resources for Mathematics ICTCM Instructor Resource Center EZ Tracker myPearsonStore ... MyMathTest Introduction to General Topology George L. Cain Georgia Institute of Technology ISBN-10: 0201756110 ISBN-13: 9780201756111 Publisher: Addison-Wesley Format: Paper Published: 09/27/2001 Suggested retail price: $73.33 Buy from myPearsonStore Request a printed exam copy Email this page to a colleague Prepare for the First Day of Class ... Sample Chapter View a Sample Chapter PDF: Promotions Promotions Instructor Resources Student Resources ... Addison-Wesley's Algebra Review Addison-Wesley Addison-Wesley's Basic Math Review Addison-Wesley Algebra Review Study Card, 2/E

18. Science Central : Science - Math - Topology - General Topology Category Listing Science Math - Topology - general topology. http://www.sciencecentral.com/category/26945

Friday, 14 March, 2008 Home Submit Science Site Add to Favorite Contact search for Directories Aeronautics and Aerospace Agriculture Anomalies and Alternative Science Astronomy ... Technology Category: Science Math Topology General Topology SUBMIT A SITE General Topology Order by Popularity Alphabet Sites Records 1-12 of 12 The Stone-Cech Compactification (Popularity: Notes by Mike Stannett. Applied General Topology (Popularity: Abstracts of all volumes. Oxford Analytic Topology Research Group (Popularity: Research interests: topology of metric spaces, generalised metric spaces, continua, function spaces, hyperspaces, topological algebra, ... Textbook in Problems on Elementary Topology (Popularity: The core of the book is the material included usually into the Topology part of ... Open Questions in Topology (Popularity: By Marianne Morillon. Moscow State University (Popularity: Department of General Topology and Geometry. Members, research interests, seminars. Mathematical Atlas: General Topology (Popularity: From Dave Rusin's "Known Math" collection. Mathematics Arxiv Front - GN General Topology (Popularity: Preprints in general topology.

19. Course 221 - General Topology And Real Analysis Course 221 general topology and Real Analysis. Lecture Notes in the Academic Year 2007-08. Available here are Draft lecture notes for the first semester http://www.maths.tcd.ie/~dwilkins/Courses/221/

Course 221 - General Topology and Real Analysis Lecture Notes in the Academic Year 2007-08 Available here are Draft lecture notes for the first semester of course 221, in 2007-08 Assignments in the Academic Year 2007-08 Students are required to complete the following assignments:- Assignment 1 [ PDF Assignment 2 [ PDF Lecture Notes in the Academic Year 2006-07 The lecture notes for course 221, as it was taught at Trinity College, Dublin, in the academic year 2006-2007, are available here. Section 1: Sets, functions and countability [ PDF Section 2: Metric spaces; [ PDF Section 3: Complete metric spaces, normed vector spaces, and Banach spaces; [ PDF Section 4: Topological spaces; [ PDF Section 5: Compact spaces; [ PDF Section 6: The extended real number system; [ PDF Section 7: Measure spaces; [ PDF Section 8: The Lebesgue integral; [ PDF Section 9: Signed measures and the Radon-Nikodym Theorem; [ PDF dwilkins@maths.tcd.ie Assignments in the Academic Year 2006-07 Students are required to complete the following assignments:- Assignment 1 [ PDF Assignment 2 [ PDF Lecture notes for undergraduate courses Dr. David R. Wilkins

20. McGraw-Hill: Schaum's Outline Of General Topology : Book Mathematics students around the world turn to this clear and complete guide to general topology for its through introduction to the subject, http://www.mhprofessional.com/product.php?cat=117&isbn=0070379882

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