Pairwise Semiregular Properties on Generalized Pairwise Lindelof Spaces

Abstract

Let $\left(X,{\tau }_1,{\tau }_2\right)$ be a bitopological space and its pairwise semiregularization. Then a bitopological property $\mathcal{P}$\ is called pairwise semiregular provided that $\left(X,{\tau }_1,{\tau }_2\right)$\ has the property $\mathcal{P}$\ if and only if $\left(X,{\tau }_{\left(1,2\right)}^s,{\tau }_{\left(2,1\right)}^s\right)$\ has the same property. In this work we study pairwise semiregular property of $\left(i,j\right)$-nearly Lindelöf, pairwise nearly Lindelöf, $\left(i,j\right)$-almost Lindelöf, pairwise almost Lindelöf, $\left(i,j\right)$-weakly Lindelöf and pairwise weakly Lindelöf spaces. We prove that $\left(i,j\right)$-almost Lindel% öf, pairwise almost Lindelöf, $\left(i,j\right)$-weakly Lindelö% f and pairwise weakly Lindelöf are pairwise semiregular properties, on the contrary of each type of pairwise Lindelöf space which are not pairwise semiregular properties.

arXiv comment10 pages, conference