Funktorialitäten für relative topologische Gruppen

Abstract: In this thesis, a right adjoint to the fibre product functor of the category of relative topological spaces with locally proper maps is constructed. After a discussion of its basic properties in chapter 3, in particular concerning its relation to the direct image functor of sheaves, it is used to formulate a version of Frobenius reciprocity in the context of continuous representations or, more generally, topological groups acting on relative topological spaces.
The definition of locally proper map has been introduced in [O. Schnürer, W. Soergel 2014]. It is a natural generalization of locally compact spaces to continuous maps. In the same vein, a separable or universally closed map is a generalization of Hausdorff spaces to continuous maps. Chapter 2 contributes strongly to the understanding of separable locally proper maps. The main result is a generalizition of the Alexandroff or one-point-compactification to continuous mappings: Every continuous map can be proprified by embedding the domain in a larger topological space and extending the map appropriately.
A corollary of this result is the characterization of separable locally proper maps as compositions of an open embedding and a separable proper map

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Deutsch
• Notes: Universität Freiburg, Dissertation, 2018

Classification and Topics

• Classification: Mathematik
• Keyword: Eigentliche Abbildung ; Stetige Abbildung ; Topologische Gruppe ; Lemma ; Offene Menge ; Kategorientheorie ; Eigentliche Abbildung ; Kategorientheorie ; Topologische Gruppe ; Adjunktion ; Faserung ; Mengentheoretische Topologie

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2018
• Creator: Gerhards, Maximilian
• Contributor: Soergel, Wolfgang ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Further information

• DOI: 10.6094/UNIFR/16008
• URN: urn:nbn:de:bsz:25-freidok-160083
• Rights: Kein Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:38 AM CEST