6533b824fe1ef96bd127fe64

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Categorically algebraic topology versus universal topology

Sergey A. Solovyov

subject

Artificial IntelligenceLogicMathematics::Category TheoryCategory of topological spacesAlgebraic topology (object)Extension topologyTopological groupGeneral topologyInitial topologyTopological spaceParticular point topologyTopologyMathematics

description

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.

yearjournalcountryeditionlanguage
2013-09-01Fuzzy Sets and Systems
https://doi.org/10.1016/j.fss.2012.10.005