New Results on Difference Paracompactness in Topological Spaces

An interesting area of research in topology is $D-$paracompact spaces. It is a significant type of topological spaces that retain compactness while benefiting from paracompactness, which it is considerd as generalisation of compact spaces. The concept of $D-$paracompactness was introduced and its basic characteristics were examined by the author in $\cite{Q17}$. In this research, we introduce and improve this concept further by using a special type of covering and the difference sets(called as $D-$sets), which contains new and impactful properties. As a result, we obtained several new properties and results. We discuss the concept, characteristics, and theorems that related of $D-$paracompact space. We also studied different characterizations of $D-$paracompact spaces and discussed how they relate to other topological characteristics. We also give numerous instances of $D-$paracompact spaces along with highlighting their applicability in different topological spaces.