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Aplikace deskriptivní teorie množin v matematické analýze / Applications of descriptive set theory in mathematical analysis

We characterize various types of σ-porosity via an infinite game in terms of winning strategies. We use a modification of the game to prove and reprove some new and older in- scribing theorems for σ-ideals of σ-porous type in locally compact metric spaces. We show that there exists a closed set which is σ-(1 − ε)-symmetrically porous for every 0 < ε < 1 but which is not σ-1-symmetrically porous. Next, we prove that the realizable by an action unitary representations of a finite abelian group Γ on an infinite-dimensional complex Hilbert space H form a comeager set in Rep(Γ, H). 1

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:327421
Date January 2013
CreatorsDoležal, Martin
ContributorsZelený, Miroslav, Holický, Petr, Zapletal, Jindřich
Source SetsCzech ETDs
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/doctoralThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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