Composite variety-based topological theories

Authors:
Sergey A. Solovyov
Affiliations:
Department of Mathematics, University of Latvia, Zellu iela 8, LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

Motivated by the recent result of Rodabaugh on categorical redundancy of lattice-valued bitopology, the paper considers another viewpoint on the topic, based on the notion of composite variety-based topological theory. The new concept, apart from providing a variable-basis generalization of bitopology, incorporates the most important approaches to topology currently developed in the fuzzy community, bringing forward their categorically algebraic properties, which are cleared from point-set lattice-theoretic dependencies. Dwelling on different ways of interaction between composite topology and topology, e.g., embedding the former into the latter as a full bicoreflective subcategory, we finally arrive at the conclusion that (variable-basis) bitopological theories still deserve to be studied on their own.