Record Nr.

UNINA9910146284703321

Autore

Todorcevic Stevo

Titolo

Topics in Topology / / by Stevo Todorcevic

Pubbl/distr/stampa


Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1997

ISBN

3-540-68338-0

Edizione

[1st ed. 1997.]

Descrizione fisica

1 online resource (VIII, 160 p.)

Collana

Lecture Notes in Mathematics, , 1617-9692 ; ; 1652

Classificazione

54C30

Disciplina

514

Soggetti

Topology

Topological groups

Lie groups

Functions of real variables

Topological Groups and Lie Groups

Real Functions

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

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.

Sommario/riassunto

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.