Abstract
The main aim of this paper is the several characterizations of pairwise fuzzy irresolvable spaces and pairwise fuzzy open hereditarily irresolvable spaces are established.
Highlights
The fuzzy sets were introduced by L.A.Zadeh [23] in 1965 and further the concept of fuzzy topological spaces was introduced by C.L.Chang [3] which is the generalization of topological spaces in 1968
A.Kandil [7] introduced the concept of fuzzy bitopological spaces in 1989 which is the generalization of fuzzy bitopological spaces and since many concepts in classical topology have been extended to fuzzy bitopological spaces
Proposition 6.4 If λ is a pairwise fuzzy dense set in a pairwise fuzzy open hereditarily irresolvable space (X, T1, T2), clTi(λ) = 1 (i = 1, 2) in (X, T1, T2)
Summary
The fuzzy sets were introduced by L.A.Zadeh [23] in 1965 and further the concept of fuzzy topological spaces was introduced by C.L.Chang [3] which is the generalization of topological spaces in 1968. Definition 5.6 A fuzzy bitopological space (X, T1, T2) is called a pairwise fuzzy open hereditarily irresolvable space if for each pairwise fuzzy somewhere dense set λ in (X, T1, T2), intTi(λ) = 0 (i = 1, 2) in (X, T1, T2). For the pairwise fuzzy somewhere dense set 1 − η in (X, T1, T2), intTi(1 − η) = 0 in (X, T1, T2) implies that (X, T1, T2) is not a pairwise fuzzy open hereditarily irresolvable space.
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