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$τ$-compactness in separated fuzzy topological spaces

In: Tatra Mountains Mathematical Publications, vol. 12, no. 3
Elena Tsiporkova - Bernard De Baets
Detaily:
Rok, strany: 1997, 99 - 112
O článku:
Natural improvements of the definitions of separated, quasi-separ ated and weakly quasi-separated fuzzy topological spaces are proposed. As a consequence, it can be shown that any compact fuzzy set (in Chang's sense) in a separated fuzzy topological space is closed. Furthermore, Lowen's fuzzy compactness is generalized to the notion of $T$-compactness, with $T$ a t-norm. In the same spirit, the notions of $S$-open and $S$-closed fuzzy sets, with $S$ a t-conorm, are introduced. It is shown that any $T$-compact fuzzy set in a separated fuzzy topological space is $T*$-closed, with $T*$ the dual t-conorm of $T$. Finally, the notions of $T$-compact, $T$-regular and $T$-normal fuzzy topological spaces are introduced, and it is shown that any separated and $W$-compact topologically generated fuzzy topological space is $W$-regular, and that any $W$-regular and $W$-compact topologically generated fuzzy topological space is $W$-normal, with $W$ the Ł ukasiewics t-norm.
Ako citovať:
ISO 690:
Tsiporkova, E., De Baets, B. 1997. $τ$-compactness in separated fuzzy topological spaces. In Tatra Mountains Mathematical Publications, vol. 12, no.3, pp. 99-112. 1210-3195.

APA:
Tsiporkova, E., De Baets, B. (1997). $τ$-compactness in separated fuzzy topological spaces. Tatra Mountains Mathematical Publications, 12(3), 99-112. 1210-3195.