Publication details
On fuzzification of topological categories
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Fuzzy Sets and Systems |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.fss.2013.05.003 |
| Field | General mathematics |
| Keywords | Approach space; Categorically-algebraic topology; Completely distributive lattice; Fuzzy topology; Powerset theory; Topological category; Topological co-axiom; Topological theory; Tower extension of topological categories; Universal topology |
| Description | This paper shows that(L, M)-fuzzy topology of U. Höhle, T. Kubiak and A. Šostak 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. |