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Topologie generované přidáváním jednotlivých bodů / Topologies generated by adding single points

We define a general notion of closure scheme to systematically study the classes of Fréchet, sequetial, (pseudo)radial, (weakly) (discretely) Whyburn, and (weakly) discretely generated spaces. First, several general propositions on closure schemes and preservation of induced properties under topological constructions are proved and later applied when we systematically summarize the properties of the classes mentioned above. Next, we focus on a detailed overview of inclusions between the classes in the general case, in the case of Hausdorff spaces, and under additional conditions like compactness and countable compactness. Valid inclusions between the classes are summarized in well arranged diagrams, invalid inclusions are demonstrated by several counterexamples.

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:332039
Date January 2014
CreatorsBartoš, Adam
ContributorsSimon, Petr, Hušek, Miroslav
Source SetsCzech ETDs
LanguageCzech
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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