6533b7ddfe1ef96bd12747b9
RESEARCH PRODUCT
On fuzzification of topological categories
Sergey A. Solovyovsubject
Connected spaceTopological algebraArtificial IntelligenceLogicMathematics::Category TheoryCategory of topological spacesGeneral topologyTopological spaceTopologyTopological vector spaceHomeomorphismMathematicsTopological categorydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-03-01 | Fuzzy Sets and Systems |