Some generalizations of pairwise Urysohn spaces
Generalizing the concept of pairwise Urysohn spaces, pairwise semi- Urysohn spaces and pairwise s-Urysohn spaces are introduced. A bitopological space (X,\({\mathcal T}_ 1,{\mathcal T}_ 2)\) is said to be pairwise semi-Urysohn (respectively, pairwise s-Urysohn if for any two distinct points x and y of X, there exists a \({\mathcal T}_ 1\)-semiopen set \(U_ 1\) and a \(\tau_ 2\)-semiopen set \(U_ 2\) such that \(x\in U_ 1\), \(y\in U_ 2\) and \({\mathcal T}_ 2\) scl \(U_ 1\cap {\mathcal T}_ 1scl U_ 2=\emptyset\) (respectively \({\mathcal T}_ 1cl U_ 2\cap {\mathcal T}_ 2cl U_ 1=\emptyset)\). We prove that the product of an arbitrary family of pairwise semi-Urysohn (respectively, pairwise s-Urysohn) spaces is pairwise semi-Urysohn (respectively, pairwise s-Urysohn). Several other properties as well as the relationships with other pairwise separation axioms of these classes of spaces are studied.
scientific article; zbMATH DE number 4019982