On $L$-almost separation axioms in $L$-fuzzifying bitopological spaces
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Khalaf and El-Latif \cite{Khalaf} introduced and investigated the concept of $L$-almost separation axioms in $L$-fuzzifying bitopological spaces, where $L$ is a complete residuated lattice, but we note that some of their results are incorrect (See Theorems 6, 7, 8, 18 in \cite{Khalaf}). Firstly in this paper we give some counterexamples to show that these results generally need not be true. Secondly, we introduced the notions of $L$-almost continuity, $L$-almost open function and $L$-completely continuous function in $L$-fuzzifying bitopological spaces with studying some important results. Finally, under these types of $L$-fuzzy mappings we study the image of these kinds of $L$-fuzzifying bitopological spaces.
Abstract
Khalaf and El-Latif \cite{Khalaf} introduced and investigated the concept of $L$-almost separation axioms in $L$-fuzzifying bitopological spaces, where $L$ is a complete residuated lattice, but we note that some of their results are incorrect (See Theorems 6, 7, 8, 18 in \cite{Khalaf}). Firstly in this paper we give some counterexamples to show that these results generally need not be true. Secondly, we introduced the notions of $L$-almost continuity, $L$-almost open function and $L$-completely continuous function in $L$-fuzzifying bitopological spaces with studying some important results. Finally, under these types of $L$-fuzzy mappings we study the image of these kinds of $L$-fuzzifying bitopological spaces.
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