广义成对Lindelof空间的成对半正则性质
Pairwise Semiregular Properties on Generalized Pairwise Lindelof Spaces
摘要：
设$\left( X,τ_{1},τ_{2}\right) $是一个双拓扑空间，$% \left( X,τ_{\left( 1,2\right) }^{s},τ_{\left( 2,1\right) }^{s}\right) $是它的成对半正则化.那么一个双拓扑性质$\mathcal{P}$ \称为成对半正则，只要$\left( X,τ_{1},τ_{2}\right) $ \具有性质$\mathcal{P}$ \当且仅当$\left( X,τ_{\left( 1,2\right) }^{s},τ_{\left( 2,1\right) }^{s}\right) $ \具有相同的性质。本文研究了$\left( i,j\right) $ -几乎Lindelöf，两两几乎Lindelöf，$\left( i,j\right) $ -几乎Lindelöf，两两几乎Lindelöf，$\left( i,j\right) $ -弱Lindelöf和两两弱Lindelöf空间的两两半正则性.证明了$\left( i,j\right) $ -almost Lindel% f，两两almost Lindelöf，$\left( i,j\right) $ -weakly Lindelöf和两两weakly Lindelöf是两两半正则性质，而每一类两Lindelöf空间不是两两半正则性质.
英文摘要：
Let $\left( X,τ_{1},τ_{2}\right) $ be a bitopological space and $% \left( X,τ_{\left( 1,2\right) }^{s},τ_{\left( 2,1\right) }^{s}\right) $ its pairwise semiregularization. Then a bitopological property $\mathcal{P}$\ is called pairwise semiregular provided that $\left( X,τ_{1},τ_{2}\right) $\ has the property $\mathcal{P}$\ if and only if $\left( X,τ_{\left( 1,2\right) }^{s},τ_{\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.
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