Tholen, Walter2016-09-132016-09-132013-06http://hdl.handle.net/10315/32010Lawvere'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.Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.Electronic Thesis or DissertationL-completenessL-complete morphismsLax algebrasTopological concepts