Topics in Topology

• Main Author: Todorcevic, Stevo (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Edition: 1st ed. 1997.
• Series: Lecture Notes in Mathematics, 1652
• Subjects: Topology.; Topological groups.; Lie groups.; Functions of real variables.; Topological Groups, Lie Groups.; Real Functions.

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 t...

Table of Contents:

• 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.