Pairwise Semiregular Properties on Generalized Pairwise Lindelof Spaces

Let $(X,{\tau }_1,{\tau }_2)$ be a bitopological space and $% \left( X,\tau _{\left( 1,2\right) }^{s},\tau _{\left( 2,1\right) }^{s}\right) $itspairwisesemiregularization\mathrm{.}Thenabitopologicalproperty$$\mathcal{P}$$
is called pairwise semiregular provided that $\left( X,\tau _{1},\tau _{2}\right) $hastheproperty$$\mathcal{P}$$ifandonlyif$\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) $-nearlyLindel\ddot{o}f,pairwisenearlyLindel\ddot{o}f,$\left( i,j\right) $-almostLindel\ddot{o}f,pairwisealmostLindel\ddot{o}f,$\left( i,j\right) $-weakly Lindel"{o}f and pairwise weakly Lindel"{o}f spaces. We prove that $(i,j)$-almost Lindel% "{o}f, pairwise almost Lindel"{o}f, $(i,j)$-weakly Lindel"{o}% f and pairwise weakly Lindel"{o}f are pairwise semiregular properties, on the contrary of each type of pairwise Lindel"{o}f space which are not pairwise semiregular properties.