Pairwise Nearly Compact and Pairwise Nearly Paracompact Spaces and it Application

摘要

In this paper, we shall introduce and study the pairwise nearly compact and paracompact bitopological spaces and investigate some of their characterizations. Moreover we study the pairwise nearly compact and pairwise nearly paracompact bitopological spaces by using (i,j)-property. Some examples and counterexamples would be provide in order to establish their properties. Furthermore the Lindelof and pairwise nearly Lindelof bitopological spaces are also discussed. Finally, we suggest some ideas to apply the spaces mention above to study the topological entropy which is using to measure the complexity of dynamical systems.