6533b7ddfe1ef96bd12747b9

RESEARCH PRODUCT

On fuzzification of topological categories

Sergey A. Solovyov

subject

Connected spaceTopological algebraArtificial IntelligenceLogicMathematics::Category TheoryCategory of topological spacesGeneral topologyTopological spaceTopologyTopological vector spaceHomeomorphismMathematicsTopological category

description

This paper shows that (L,M)-fuzzy topology of U. Hohle, T. Kubiak and A. Sostak is an instance of a general fuzzification procedure for topological categories, which amounts to the construction of a new topological category from a given one. This fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of D. Zhang, thereby providing the procedure of tower extension of topological categories. With the help of this dualization, we arrive at the meta-mathematical result that the concept of (L,M)-fuzzy topology and the notion of approach space of R. Lowen are ''dual'' to each other.

https://doi.org/10.1016/j.fss.2013.05.003