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On semi star generalized closed sets in bitopological spaces. (English) Zbl 1211.54044

A subset \(A\) of a bitopological space \((X,\tau_1,\tau_2)\) is called \(\tau_1\tau_2\)-semi star generalized closed (briefly \(\tau_1\tau_2\)-\(s^*g\) closed) if \(\tau_2\)-\(cl(A)\subseteq U\) whenever \(A\subseteq U\) and \(U\) is \(\tau_1\)-semi open in \(X\). Then a map \(f:(X,\tau_1,\tau_2)\rightarrow (Y,\sigma_1,\sigma_2)\) is said to be pairwise \(s^*g\)-continuous if \(f^{-1}(U)\) is \(\tau_i\tau_j\)-\(s^*g\) closed for each \(\sigma_j\)-closed set \(U\) in \(Y\) (\(i\neq j\), \(i,j=1,2\)). In the paper the authors present some straightforward results for \(\tau_1\tau_2\)-\(s^*g\) closed sets and pairwise \(s^*g\)-continuous mappings and introduce the concepts of \(S^*GO\)-connectedness and \(S^*GO\)-compactness for bitopological spaces.

MSC:

54E55 Bitopologies
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