Exploring Properties of D-Lindelöf Bitopological Spaces and Their Relations to D-Compact Spaces

Abstract

This paper introduces the fundamental concepts of D-sets and discuss their properties,
including D-Lindelöfness and D-countably compactness. we introduce the basic notions of
bitopological spaces, along with relevant definitions and examples, including compactness, P*
compactness, S*-compactness, and P*-countably compactness and their properties.
Our research focuses and investigates the properties of D-Lindelöf bitopological spaces, as well as
𝑃∗ − D −Lindelöf, 𝑆∗ −D−Lindelöf and D-Lindelöf spaces. We also explore D-countably
compact, 𝑃∗ − D −countably compact and 𝑆∗ − D −countably compact spaces. Additionally, we
examine the relationships between these properties and provide examples to highlight their
differences.