Elsevier

Fuzzy Sets and Systems

Volume 227, 16 September 2013, Pages 25-45
Fuzzy Sets and Systems

Categorically algebraic topology versus universal topologyI

https://doi.org/10.1016/j.fss.2012.10.005Get rights and content

Abstract

This paper continues to develop the theory of categorically algebraic (catalg) topology, introduced as a common framework for the majority of the existing many-valued topological settings, to provide convenient means of interaction between different approaches. Motivated by the results of universal topology of H. Herrlich, we show that a concrete category is fibre-small and topological if and only if it is concretely isomorphic to a subcategory of a category of catalg topological structures, which is definable by topological co-axioms.

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    I

    This research was supported by the ESF Project No. CZ.1.07/2.3.00/20.0051 "Algebraic methods in Quantum Logic" of the Masaryk University in Brno, Czech Republic.

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