Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

Author: Lynn Arthur Steen

Publisher: Courier Corporation

ISBN: 9780486319292

Category: Mathematics

Page: 272

View: 841

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

In this book the author has attempted to present such counterexamples in topological vector spaces, ordered topological vector spaces, topological bases
and topological algebras. The author makes no claim to completeness, obviously
...

Introduction The theory of the projective topology in tensor product spaces was
established by Grothendieck in ( 3 ) . Since then it has ... Grothendieck called this
question " Problème des topologies ” . We shall construct counterexamples to it .

What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress.

Author: Bernard R. Gelbaum

Publisher: Springer Science & Business Media

ISBN: 9781461209935

Category: Mathematics

Page: 305

View: 639

The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.

The frequency spectrum of a topological space and the product operation. Tr.
Mosk. Mat. ... Some properties of C(X), I. Topology Appl. 14: 151-161. 7. Gillman,
L. & M. Jerison ... Counterexamples in Topology (Second edition). Springer-
Verlag.

Author: Michael G. CharalambousPublish On: 2019-10-08

This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case.

Author: Michael G. Charalambous

Publisher: Springer Nature

ISBN: 9783030222321

Category: Mathematics

Page: 261

View: 663

This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.

J. W. Keesee , An introduction to algebraic topology , Brooks / Cole , Belmont ,
Calif . , 1970 . 21. J. L. Kelley ... Steen and A. J. Seebach , Jr. , Counterexamples in topology , Holt , Rinehart and Winston , New York , 1970 . 32. C. T. C. Wall , A ...

SCHUBERT , H . Topology . Boston : Allyn and Bacon , Inc . , 1968 . SIERPINSKI ,
W . General Topology . Toronto : University of Toronto Press , 1952 . STEEN , L .
A . , and J . A . SEEBACH . Counterexamples in Topology . New York : Holt ...

R.E. Hodel , Cardinal functions I , in " Handbook of Set - theoretic Topology , " ( K.
Kunen and J.E. Vaughan , eds . ) Elsevier Science Publishers B.V. , North
Holland , 1984 , pp . 1-61 . 12. L.A. Steen and J.A. Seebach , “ Counterexamples in ...

Author: Kossuth Lajos Tudományegyetem. Matematikai IntézetPublish On: 1980

Attila Pethő L. A. Steen - J . A. Seebach , Jr. , Counterexamples in Topology .
Second Edition . xi + 244 pages ... A counterexample , in its most restricted sense
, is an example which disproves a conjecture . The authors choose to interpret
the ...

Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet

Some Notes on Computer Generation of Counterexamples in Topology. ... In [2]
we describe a method of representing some topological theorems which seems
to have enough power of expression to be of real value to a mechanical
topologist ...

In this chapter we present counterexamples related to several different concepts
involving convergence in probability ... The weak* topology on P is the topology
with a neighborhood base consisting of all sets of the form s.som-soo. with pi e P,
...

Author: Gary L. Wise

Publisher: Oxford University Press

ISBN: 019536130X

Category: Mathematics

Page: 224

View: 297

A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas in mathematical sciences that might seem intuitively obvious may be proved incorrect with the use of a counterexample. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among such treatments. The authors argue convincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessible for the first time. In contrast to several other collections, all of the examples in this book are completely self-contained--no details are passed off to obscure outside references. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will want a copy of this book.

Steen , L . A . , and J . A . Seebach , Jr . Counterexamples in Topology . New York
: Holt , Rinehart , and Winston , 1970 . 210p . Contents : General introduction .
Separation axioms . Compactness . Connectedness . Metric spaces .

G. Köthe , Topological vector spaces . I , Springer , 1969 . 5. K. McKennon and
J. M. Robertson , Locally convex spaces , Dekker , New York , 1976 . 6. L. A.
Steen and J. A. Seebach , Counterexamples in topology , Springer , 1978 . 7.

46Axx.0004 83j : 22001 Roelcke , Walter , Dierolf , Susanne * Uniform structures
on topological groups and their quotients . Advanced Book ... 46Axx.0005 84a :
46002 Khaleelulla , S. M. Counterexamples in topological vector spaces . Lecture
...