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1	A Relational Localisation Theory for Topological Algebras Schneider, Friedrich Martin 07 August 2012 (has links) (PDF) In this thesis, we develop a relational localisation theory for topological algebras, i.e., a theory that studies local approximations of a topological algebra’s relational counterpart. In order to provide an appropriate framework for our considerations, we first introduce a general Galois theory between continuous functions and closed relations on an arbitrary topological space. Subsequently to this rather foundational discussion, we establish the desired localisation theory comprising the identification of suitable subsets, the description of local structures, and the retrieval of global information from local data. Among other results, we show that the restriction process with respect to a sufficiently large collection of local approximations of a Hausdorff topological algebra extends to a categorical equivalence between the topological quasivariety generated by the examined structure and the one generated by its localisation. Furthermore, we present methods for exploring topological algebras possessing certain operational compactness properties. Finally, we explain the developed concepts and obtained results in the particular context of three important classes of topological algebras by analysing the local structure of essentially unary topological algebras, topological lattices, and topological modules of compact Hausdorff topological rings. topologische Algebra Lokalisierung relationale Strukturen Galoisverbindung topological algebra localisation relational structures Galois connection ddc:510 rvk:SK 300
2	When graph meets diagonal: an approximative access to fixed point theory / Wenn der Graph auf die Diagonale trifft: ein approximativer Zugang zur Fixpunkttheorie Okon, Thomas 25 August 2001 (has links) (PDF) The thesis deals with a general access to topological transversality in uniform spaces. / Die Arbeit behandelt einen allgemeinen Zugang zur Topologischen Transversalität in uniformen Räumen. Fixpunkttheorie Nichtlinare Alternative Robertssche Räume Topologische Transversalität mengenwertige Abbildung uniformer Raum Überstreichsatz fixed point theory nonlinear alternative roberts spaces set-valued map sweeping theorem topological transversality uniform space ddc:27 rvk:SK 300 Fixpunkttheorie Mengenwertige Abbildung Uniformer Raum

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A Relational Localisation Theory for Topological Algebras

When graph meets diagonal: an approximative access to fixed point theory / Wenn der Graph auf die Diagonale trifft: ein approximativer Zugang zur Fixpunkttheorie