$p$-$\mathcal{I}$-generator and $p_1$-$\mathcal{i}$-generator in bitopology

Abstract

In this article we have investigated the relations of $p$-$\mathcal{I}$-generator, $p_1$-$\mathcal{I}$-generator with $p$-Lindel\"{o}f and $p_1$-Lindel\"{o}f using $\tau_i$-codense, $(i,j)$-meager, $(i,j)$-nowhere dense and perfect mapping of bitopological space. The relations between $p$-compactness, $p$-Lindel\"{o}fness, $p_1$-Lindel\"{o}fness and topological ideal, $(i,j)$-meager, $(i,j)$-Baire space in bitopological space are investigated. Some properties are studied on product bitopology using perfect mapping. It can be found that bitopological space has many applications in real life problems. Hence, we hope that this theory will help to fulfill some interlinks which may have applications in near future.