Topics in Topology

Stevo Todorcevic (auth.)3540626115, 9783540626114

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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Table of contents :
Compact sets in function spaces….Pages 1-60
The semigroup βℕ….Pages 61-78
Compact and compactly generated groups….Pages 79-120
Hyperspaces….Pages 121-147