The book describes some interactions of topology with other areas of mathematics and it requires only basic background. The first chapter deals with the topology of pointwise convergence and proves results of Bourgain, Fremlin, Talagrand and Rosenthal on compact sets of Baire class-1 functions. In the second chapter some topological dynamics of beta-N and its applications to combinatorial number theory are presented. The third chapter gives a proof of the Ivanovskii-Kuzminov-Vilenkin theorem that compact groups are dyadic. The last chapter presents Marjanovic's classification of hyperspaces of compact metric zerodimensional spaces.

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Bibliographic Information

Book Title: Topics in Topology
Authors: Stevo Todorcevic
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0096295
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1997
Softcover ISBN: 978-3-540-62611-4Published: 20 March 1997
eBook ISBN: 978-3-540-68338-4Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 160
Topics: Topology, Topological Groups, Lie Groups, Real Functions

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Table of contents (4 chapters)

Front Matter

Compact sets in function spaces

The semigroup βℕ

Compact and compactly generated groups

Hyperspaces

Back Matter

About this book