21. MATH525 - Topics In TopologyII: Topological Groups Search by CID Academic Year 2002/2003 Topics in TopologyII TopologicalGroups MATH 525 FA. The course has two components, as follows http://www.wesleyan.edu/course/math525f.htm

document.domain="wesleyan.edu"; Wesleyan Home Page WesMaps Home Page WesMaps Archive Course Search ... Course Search by CID Academic Year 2002/2003 Topics in TopologyII: Topological Groups MATH 525 FA The course has two components, as follows: (I) (about seven weeks) An introductory survey of the basic definitions and some of the fundamental results, including perhaps the theorems of Kakutani-Kodaira, Pontrjagin, Haar, and Kuzminov-Ivanovskii. (II) (about six weeks) More modern material relating to the topological structure of topological groups, with emphasis upon cardinal invariants and the current status of selected unsolved problems concerning Lindelof groups, pseudocompact groups, countably compact groups, van der Waerden groups, and free topological groups. Note: This course has been offered frequently in the past under the designation Math 533. MAJOR READINGS E. Hewitt and K. A. Ross, ABSTRACT HARMONIC ANALYSIS VOL I, Springer-Verlag, 1963 D. Dikranjan, I. R. Prodanov, and L. N. Stoyanov, TOPOLOGICAL GROUPS, Marcel Dekker, Inc. 1990 EXAMINATIONS AND ASSIGNMENTS Routine homework problems will be assigned, and more difficult questions will be proposed for consideration.

22. The Concentration Phenomenon And Topological Groups By Vladimir Pestov The concentration phenomenon and topological groups. Vladimir Pestov. Invited Contribution.Introduction. 29 V. Pestov, topological groups Where to from here? http://at.yorku.ca/t/a/i/c/35.htm

Topology Atlas Document # taic-35 Topology Atlas Invited Contributions vol. 5 issue 1 (2000) 5-10 The concentration phenomenon and topological groups Vladimir Pestov Invited Contribution Introduction The phenomenon of concentration of measure on high-dimensional structures [ ] (also known as the geometric law of large numbers) is an important development in modern analysis and geometry, manifesting itself across a wide range of mathematical sciences, particulaly geometric functional analysis [ ], probability theory [ ], graph theory [ ], diverse fields of computer science [ ], and statistical physics [ Some of the most interesting recent developments related to concentration of measure occured in topological groups and compact G-spaces. The present author believes that those are only the tip of an iceberg and the potential for interaction of the phenomenon with topology is far greater than that, so that concentration deserves to be better known among topologists. Overview n S n . However, his results lay dormant until about 1970, when Vitali Milman [ ] realized that the famous Dvoretzky's Theorem on almost spherical sections of convex bodies is a manifestation of the concentration phenomenon on spheres. The paper [

23. Strongly Extraresolvable Topological Groups By W. W. Comfort And Salvador Garc\' rights reserved. Strongly Extraresolvable topological groups. WWComfort and Salvador GarcíaFerreira. Research Announcement. For http://at.yorku.ca/i/a/a/c/53.htm

Topology Atlas Document # iaac-53 Strongly Extraresolvable Topological Groups Research Announcement T T 'subset or equal' X, int X cl X strongly extraresolvable if there is a family D D D The authors show: Every product of infinitely many nontrivial separable metric spaces admits a dense strongly extraresolvable subspace. Every nondiscrete locally compact group has a dense strongly extraresolvable subset. A completed manuscript is available from the authors. Authors' addresses: W. W. Comfort, Wesleyan University, Middletown, CT, 06459 USA email: wcomfort@wesleyan.edu email: garcia@servidor.unam.mx Mathematics Subject Classification: 22A05, 54A05, 54H11 Notes: See follow-up Dense Subsets of Maximally Almost Periodic Groups Date Received: February 10, 1998 Topology Atlas

24. The Definition And Basic Properties Of Topological Groups The Definition and Basic Properties of topological groups. Artur KornilowiczUniversity of Bialystok. On the topological groups. Bibliography. http://mizar.uwb.edu.pl/JFM/Vol10/topgrp_1.html

Journal of Formalized Mathematics Volume 10, 1998 University of Bialystok Association of Mizar Users The Definition and Basic Properties of Topological Groups Artur Kornilowicz University of Bialystok MML Identifier: The terminology and notation used in this paper have been introduced in the following articles [ Contents (PDF format) Preliminaries On the Groups On the Topological Spaces The Group of Homeomorphisms On the Topological Groups Bibliography 1] Jozef Bialas and Yatsuka Nakamura. Dyadic numbers and T$_4$ topological spaces Journal of Formalized Mathematics 2] Leszek Borys. Paracompact and metrizable spaces Journal of Formalized Mathematics 3] Czeslaw Bylinski. Binary operations Journal of Formalized Mathematics 4] Czeslaw Bylinski. Functions and their basic properties Journal of Formalized Mathematics 5] Czeslaw Bylinski. Functions from a set to a set Journal of Formalized Mathematics 6] Czeslaw Bylinski. Some basic properties of sets Journal of Formalized Mathematics 7] Agata Darmochwal. Compact spaces Journal of Formalized Mathematics 8] Agata Darmochwal.

25. Categories: Re: Abelian Topological Groups categories Re Abelian topological groups. To categories@mta.ca; Subject categoriesRe Abelian topological groups; From Michael Barr barr@barrs.org ; http://north.ecc.edu/alsani/ct01(5-8)/msg00001.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Re: Abelian Topological Groups To categories@mta.ca Subject : categories: Re: Abelian Topological Groups From barr@barrs.org Date : Wed, 2 May 2001 06:11:51 -0400 (EDT) In-Reply-To 200105010437.f414bIi14109@transbay.net Sender cat-dist@mta.ca References categories: Abelian Topological Groups From: Prev by Date: categories: Abelian Topological Groups Next by Date: categories: diaxydoc.tex Prev by thread: categories: Abelian Topological Groups Next by thread: categories: diaxydoc.tex Index(es): Date Thread

26. Categories: Abelian Topological Groups categories Abelian topological groups. To categories@mta.ca; Subject categoriesAbelian topological groups; From Bill Rowan rowan@transbay.net ; http://north.ecc.edu/alsani/ct01(5-8)/msg00000.html

[Date Prev][ Date Next ][Thread Prev][ Thread Next Date Index Thread Index categories: Abelian Topological Groups To categories@mta.ca Subject : categories: Abelian Topological Groups From rowan@transbay.net Date : Mon, 30 Apr 2001 21:37:18 -0700 (PDT) Sender cat-dist@mta.ca Follow-Ups categories: Re: Abelian Topological Groups From: Next by Date: categories: Re: Abelian Topological Groups Next by thread: categories: Re: Abelian Topological Groups Index(es): Date Thread

27. Compactifications Of Topological Groups By Vladimir Uspenskij Topology Atlas Document ppae30. Compactifications of topological groups. VladimirUspenskij. Proceedings of the Ninth Prague Topological Symposium (2001) pp. http://www.emis.de/proceedings/TopoSym2001/30.htm

Topology Atlas Document # ppae-30 Compactifications of topological groups Vladimir Uspenskij Proceedings of the Ninth Prague Topological Symposium (2001) pp. 331-346 Every topological group G has some natural compactifications which can be a useful tool of studying G. We discuss the following constructions: the greatest ambit S(G) is the compactification corresponding to the algebra of all right uniformly continuous bounded functions on G; the Roelcke compactification R(G) corresponds to the algebra of functions which are both left and right uniformly continuous; the weakly almost periodic compactification W(G) is the enveloping compact semitopological semigroup of G (`semitopological' means that the multiplication is separately continuous). The universal minimal compact G-space X=M G is characterized by the following properties: X has no proper closed G-invariant subsets; A group G is extremely amenable , or has the fixed point on compacta property, if M G is a singleton. We discuss some results and questions by V. Pestov and E. Glasner on extremely amenable groups. The Roelcke compactifications were used by M. Megrelishvili to prove that W(G) can be a singleton. They can be used to prove that certain groups are minimal. A topological group is

28. Compactifications Of Topological Groups By Vladimir Uspenskij (AtlasImage Versio Topology Atlas Document ppae30 Compactifications of topologicalgroups. Vladimir Uspenskij. FIRST page LAST page Pages 1 2 3 http://www.emis.de/proceedings/TopoSym2001/30.aim/

Topology Atlas Document # ppae-30 Compactifications of topological groups Vladimir Uspenskij FIRST LAST page Pages: Back to the abstract of this document. Information about this document format

29. Atlas: Productive Properties In Topological Groups By Michael G. Tkacenko Productive Properties In topological groups presented by MichaelG. Tkacenko UAM, Iztapalapa, Mexico We present a survey of old http://atlas-conferences.com/c/a/a/o/40.htm

Atlas Document # caao-40 The 12th Summer Conference on General Topology and its Applications August 12-16, 1997 Nipissing University North Bay, ON, Canada Conference Organizers Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali and Stephen Watson View Abstracts Conference Homepage Productive Properties In Topological Groups presented by Michael G. Tkacenko UAM, Iztapalapa, Mexico We present a survey of old and new results on preservation of certain topological properties under the product operation in topological groups. Many topological properties such as compactness, connectedness, etc., are productive in the class of all topological spaces. The first productive property specific for topological groups was discovered in 1966 by Comfort and Ross [CR]: any cartesian product of pseudocompact topological groups is pseudocompact. Surprisingly, it turns out that countable compactness, intermidiate between compactness and pseudocompactness, is not productive (at least under CH or MA), the result due to van Douwen [vD]. We will present several ``relative" properties (reflecting how a subspace is embedded in the whole space) which are proved to be productive in topological groups. Let us say that a subset Y of a space X is

30. Atlas: Suitable Sets For Topological Groups By Sidney Morris Conference Organizers Anthony Hager View Abstracts. Suitable Sets for TopologicalGroups presented by Sidney Morris University of Wollongong http://atlas-conferences.com/c/a/a/g/03.htm

Atlas Document # caag-03 The Curacao Comfort Conference on Set-Theoretic Topology June 17-21, 1996 Conference Organizers Anthony Hager View Abstracts Suitable Sets for Topological Groups presented by Sidney Morris University of Wollongong In this talk I survey some results on suitable sets for topological groups due to Karl Heinrich Hofmann (who wishes he could have been here, but sends warm regards to all and to Wis Comfort, in particular), Joan Cleary, Wis Comfort, Mikhail Tkachenko, Sergey Svetlichny, Des Robbie and me. Date received: May 31, 1996 The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc.

31. A Course On Topological Groups/K. Chandrasekharan A Course on topological groups/K. Chandrasekharan. New Delhi, HindustanBook Agency, 1996, viii, 118 p., ISBN 8185931-10-0. Contents http://www.vedamsbooks.com/no27284.htm

A Course on Topological Groups/K. Chandrasekharan. New Delhi, Hindustan Book Agency, 1996, viii, 118 p., ISBN 81-85931-10-0. Contents: 1. Topological preliminaries. 2. The Haar measure on a locally compact group. 3. Hilbert spaces and the spectral theorem. 4. Compact groups and their representations. Index. "This book contains the author’s notes for a course by him at Eidgenossische Technische Hochschule, Zurich. The aim is to lead the reader to a proof of the Peter-Weyl theorem, the basic theorem in the representation theory of compact topological groups. The topological, analytical, and algebraic groundwork needed for the proof is provided as part of the course. Return to Main Catalogue Page

32. Topology: An Introduction With Application To Topological Groups Click to enlage Topology An Introduction with Application to TopologicalGroups George McCarty. Our Price, $12.95. Availability In Stock. http://store.doverpublications.com/0486656330.html

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33. Introduction To Topology: Third Edition Topology An Introduction with Application to topological groups by George McCartyCovers sets and functions, groups, metric spaces, topologies, topological http://store.doverpublications.com/0486663523.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Astronomy Biology and Medicine Bridge and Other Card Game...... Chemistry Chess Children Consumer Catalogs Cookbooks, Nutrition Crafts Detective Stories, Science...... Dover Phoenix Editions Earth Science Engineering Ethnic Interest Features Science Gift Certificates Gift Ideas Giftpack History, Political Science...... Holidays Humor Languages And Linguistics Literature Magic, Legerdemain Mathematics Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy And Religion Photography Physics Psychology Puzzles, Amusement, Recrea...... Reference Specialty Stores Sports, Out-of-door Activi...... Science and Mathematics Stationery, Gift Sets Summer Fun Shop Travel and Adventure Women's Studies By Subject Science and Mathematics Mathematics Topology Introduction to Topology: Third Edition Bert Mendelson Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 An undergraduate introduction to the fundamentals of topology — engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.

34. Topological Groups topological groups. BT group theory(maths) FT groupe topologiquePrevious Item Next Item Search Help. http://www.nrc.ca/irc/thesaurus/topological_groups.html

topological groups BT group theory(maths) FT groupe topologique [Previous Item] [Next Item] [Search] [Help]

35. Description Of Courses topological groups. V2, Fr, 9.5011.30, 10/165, 16.4. Circle of Ideas The theorieof topological groups connects the group theory with topological attributes. http://www.mathematik.tu-darmstadt.de/Math-Net/Lehrveranstaltungen/SS1999/Haupts

Third Year and Upwards Offered in the Summersemester 1999 Topological Groups Go backward to Grundgleichungen der mathematischen Physik (Feldtheorie) Go up to Advanced level courses and exercise courses in the main Topological Groups Fr Responsible Instructor: Format of Course: Lecture 2+0 Group Targeted: Students of Mathematics and Physics after the Vordiplom Prerequisites: Stuff of the undergraduate courses Circle of Ideas: The theorie of topological groups connects the group theory with topological attributes. In particular, one demands an additional attribute for the group operations, namely the continuity. Prominent represantatives of topological groups are matrix groups, but the theorey contains a substantial larger class of groups Moreover, the theory of topological groups is the foundation for the theory of Lie groups. Contents: Concepts of the topology needed for topological groups, definition and theorems for general topological groups, linear groups and transformation groups, locally compact groups, integration on locally compact spaces, the group algebra, the dual group Goals: Introduction into the methods and problems of topological groups Literature: Dieter Lutz

36. 22-XX 22XX topological groups, Lie groups. {For transformation groups,see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43 http://www.ams.org/mathweb/msc1991/22-XX.html

22-XX Topological groups, Lie groups 58-XX . For abstract harmonic analysis, see 43-XX 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 22-01 Instructional exposition (textbooks, tutorial papers, etc.) 22-02 Research exposition (monographs, survey articles) 22-03 Historical (must be assigned at least one classification number from Section 01) 22-04 Explicit machine computation and programs (not the theory of computation or programming) 22-06 Proceedings, conferences, collections, etc. ; for dual spaces of operator algebras and topological groups, see Locally compact abelian groups (LCA groups) 22C05 Compact groups Locally compact groups and their algebras ; for analysis thereon, see Top level of Index

37. 22-XX 22XX topological groups, Lie groups,. {For transformation groups,See 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, See 43 http://www.ma.hw.ac.uk/~chris/MR/22-XX.html

22-XX Topological groups, Lie groups, 58-XX . For abstract harmonic analysis, See 43-XX 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 22-01 Instructional exposition (textbooks, tutorial papers, etc.) 22-02 Research exposition (monographs, survey articles) 22-03 Historical (must be assigned at least one classification number from 01-XX 22-04 Explicit machine computation and programs (not the theory of computation or programming) 22-06 Proceedings, conferences, collections, etc. 22Axx Topological and differentiable algebraic systems, ; for dual spaces of operator algebras and topological groups, See 22Bxx Locally compact abelian groups (LCA groups) 22C05 Compact groups 22Dxx Locally compact groups and their algebras 22Exx Lie groups, 57-XX 43-XX ... Top level of Index

38. 22Axx {For topological rings and fields, see 12Jxx, 13Jxx, 16W80; for dualspaces of operator algebras and topological groups, See 47D35} http://www.ma.hw.ac.uk/~chris/MR/22Axx.html

22Axx Topological and differentiable algebraic systems, ; for dual spaces of operator algebras and topological groups, See 22A05 Structure of general topological groups 22A10 Analysis on general topological groups 22A15 Structure of topological semigroups 22A20 Analysis on topological semigroups 22A22 Topological groupoids (including differentiable and Lie groupoids) 22A25 Representations of general topological groups and semigroups 22A30 Other topological algebraic systems and their representations 22A99 None of the above but in this section Top level of Index Top level of this Section

39. Seminar Fall2000 210300. RH 202. Kevin Scannell. topological groups acting on Hyperbolic Space.Abstract We will study topological groups as they act on hyperbolic groups. http://euler.slu.edu/Dept/oldseminars/seminar_fall2000.html

FALL 2000 DATE SEMINAR TIME ROOM SPEAKER TITLE Th Sep 7 topology / geometry RH 142 Bryan Clair L - Invariants Abstract Betti numbers, first considered by Atiyah in 1976. Like the ordinary Betti numbers of a compact space, the L Betti numbers are the dimension of a homology group. However, the homology groups coming from L -forms are infinite dimensional Hilbert spaces, so the machinery of von Neumann algebras is needed to provide a quantitative dimension. I will spend the first lecture on background material, and basic examples, with some older theorems and big conjectures thrown in for spice. Don't worry if you don't know anything about von Neumann algebras. I plan to talk about Gromov's result that the L Betti numbers vanish when X is aspherical and G is amenable. I'll prove Luck's theorem, which says that ordinary Betti numbers (renormalized) of a tower of covering spaces converge to the L Betti numbers of the limit covering. I will also discuss more refined L

40. Seminars-spring2001 Kevin Scannell. topological groups acting on Hyperbolic Space. Abstract We willcontinue our study of topological groups as they act on hyperbolic groups. http://euler.slu.edu/Dept/oldseminars/seminars-spring2001.html

Seminars: SPRING 2001 DATE SEMINAR TIME ROOM SPEAKER TITLE Wed Jan 31 Topology / Geometry RH 211 Kevin Scannell Bianchi Groups Fri Feb 2 Topology/ Analysis RH 320 Kevin Scannell Topological Groups acting on Hyperbolic Space Abstract : We will continue our study of topological groups as they act on hyperbolic groups. The text we are using is by Elstrodt, Grunewald and Mennicke and is published by Springer Verlag. Tues. Feb 6 Algebra RH 134 Julianne Rainbolt Images and extensions of periodic linear groups Wed. Feb 7 Topology / Geometry RH 211 Anneke Bart Reflective Subgroups of Bianchi Groups Fri Feb 9 Topology/ Analysis RH 320 Kevin Scannell Topological Groups acting on Hyperbolic Space Tues Feb 13 Algebra RH 134 Julianne Rainbolt Images and extensions of periodic linear groups Wed Feb 14 Topology / Geometry RH 211 Anneke Bart Reflective Subgroups of Bianchi Groups Fri Feb 16 Topology/ Analysis RH 218 Kevin Scannell Topological Groups acting on Hyperbolic Space Tue Feb 20 Math Club RH 223 Kevin Scannell The Topology of the Universe Fri Feb 23 Topology/ Analysis RH 218 Kevin Scannell Topological Groups acting on Hyperbolic Space Tues Feb 27 Algebra RH 134 Greg Marks Distributive Lattices within Groups, Rings, and Modules

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