A topological theory of (T,V)-categories

dc.contributor.advisor	Tholen, Walter
dc.creator	Sozubek, Serdar
dc.date.accessioned	2016-09-13T13:15:21Z
dc.date.available	2016-09-13T13:15:21Z
dc.date.copyright	2013-06
dc.degree.discipline	Mathematics & Statistics
dc.degree.level	Doctoral
dc.degree.name	PhD - Doctor of Philosophy
dc.description.abstract	Lawvere's notion of completeness for quantale-enriched categories has been extended to the theory of lax algebras under the name of L-completeness. In this work we introduce the corresponding morphism concept and examine its properties. We explore some important relativized topological concepts like separation, density, compactness and compactification with respect to L-complete morphisms. We show that separated L-complete morphisms belong to a factorization system. Moreover, we investigate relativized topological concepts with respect to maps that preserve L-closure which is the natural symmetrized closure for lax algebras. We provide concrete characterizations of Zariski closure and Zariski compactness for approach spaces.
dc.identifier.uri	http://hdl.handle.net/10315/32010
dc.rights	Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subject.keywords	L-completeness
dc.subject.keywords	L-complete morphisms
dc.subject.keywords	Lax algebras
dc.subject.keywords	Topological concepts
dc.title	A topological theory of (T,V)-categories
dc.type	Electronic Thesis or Dissertation

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