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Die Kategorie der kompakt-erzeugten Räumeals in Top coreflektive Kategorie mit Exponentialgesetz

Breger, Herbert

English Title: The category of compactly-generated T2-spaces as in Top coreflective category with exponential law

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Abstract

Die coreflektiven Hüllen K(i) in Top von jeder der folgenden Klassen (i) topologischer Räume werden untersucht: (i) alle kompakten Räume (ii) alle quasikompakten regulären Räume (iii) alle lokal-quasikompakten Räume (iv) alle quasikompakten Räume Für jedes (i), sind die K(i)-Hausdorff Räume genau die kompakt erzeugten Räume. Außerdem sind K(1)=K(2) und K(3) cartesisch abgeschlossen, nicht jedoch K(4). (Zitat aus Herrlich/Strecker: Categorical Topology - Its Origins, in: Handbook of the History of General Topology, vol. 1, ed.: Aull/Lowen, Dordrecht, Boston, London 1997, p. 288)

Translation of abstract (English)

The coreflective hulls K(i) in Top of each of the following classes (i) of topological spaces are investigated: (i) all compact spaces (ii) all quasi-compact regular spaces (iii) all locally quasi-compact spaces (iv) all quasi-compact spaces For each (i), the K(i)-Hausdorff spaces are precisely the k-spaces. Moreover K(1)=K(2) and K(3) are cartesian closed, whereas K(4) is not. (Quotation from Herrlich/Strecker: Categorical Topology - Its Origins, in: Handbook of the History of General Topology, vol. 1, ed.: Aull/Lowen, Dordrecht, Boston, London 1997, p. 288)

Item Type: Master's thesis
Date Deposited: 29 Jan 2010 08:47
Date: 1971
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Topologische Kategorie, Koreflexion, Kelley-Raum
Uncontrolled Keywords: k-space , Kelley space , coreflexion , categorical topology
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