Topics in Topology

Häftad, Engelska, 1997

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Describing some interactions of topology with other areas of mathematics, this text assumes only a basic knowledge of the subject. 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 hyper-spaces of compact metric zerodimensional spaces.

Produktinformation

Utgivningsdatum1997-03-20
Mått155 x 235 x 10 mm
Vikt265 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Mathematics
Antal sidor160
Upplaga1997
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540626114

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Contents: Topology of pointwise convergence.- A theorem of Eberlein.- Ptak's Lemma.- Namioka's theorem.- Rosenthal's theorem.- Properties of Baire and Ramsey.- Baire property of analytic sets.- Baire property of filters and ideals.- Selective coideals.- Baire's characterization theorem and its corollaries.- Borel sets.- A selective analytic ideal.- Bourgain-Fremlin-Talagrand's theorem.- A space of ultrafilters.- Glazer's theorem.- A topological proof of van der Waerden theorem.- A semigroup of variable words.- Countable chain conditions of topological groups.- Michael's selection theorem.- Inverse systems.- Haydon's theorem.- Quotient groups.- A decomposition of compact groups.- Pestov's theorems.- Free topological groups.- Exponentially complete spaces.- Vaught's homeomorphism theorem.- Resolving a space: Accumulation orders and spectra.- Accumulation spectra of hyperspaces.- List of all exponentials.- Multiplication of accumulation orders.