Fuzzy bitopological spaces and fuzzy quasi-proximities. (English) Zbl 0589.54013
Interval and fuzzy mathematics, Proc. Polish Symp., Poznań/Pol. 1983, 115-123 (1985).
Summary: [For the entire collection see Zbl 0587.00015.]
Motivated by the fact that there are some non-symmetric fuzzy topological structures, we introduce the bitopological aspect in the theory of fuzzy bitopological spaces. We are concerned with fuzzy bitopological spaces related to fuzzy quasi-proximity spaces. We prove that a fuzzy bitopological space admits a fuzzy quasi-proximity iff it is pairwise fuzzy completely regular. We show also that every fuzzy topological space can be derived from a fuzzy quasi-proximity space. A fuzzy bitopological space version of Urysohn’s lemma is also given.
Motivated by the fact that there are some non-symmetric fuzzy topological structures, we introduce the bitopological aspect in the theory of fuzzy bitopological spaces. We are concerned with fuzzy bitopological spaces related to fuzzy quasi-proximity spaces. We prove that a fuzzy bitopological space admits a fuzzy quasi-proximity iff it is pairwise fuzzy completely regular. We show also that every fuzzy topological space can be derived from a fuzzy quasi-proximity space. A fuzzy bitopological space version of Urysohn’s lemma is also given.
