Let $\left( X,\tau _{ 1},\tau _{ 2}\right) $ be a bitopological space and $% \left( X,\tau _{ \left( 1,2\right) }^{ s},\tau _{ \left( 2,1\right) }^{ s}\right) $ 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 Lindel\"{ o}f, pairwise nearly Lindel\"{ o}f, $\left( i,j\right) $-almost Lindel\"{ o}f, pairwise almost Lindel\"{ o}f, $\left( i,j\right) $-weakly Lindel\"{ o}f and pairwise weakly Lindel\"{ o}f spaces. We prove that $\left( i,j\right) $-almost Lindel% \"{ o}f, pairwise almost Lindel\"{ o}f, $\left( i,j\right) $-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.
Categories: math.GN