New Generalizations of Pairwise Lindelöf Spaces

This study is introducing two new different pairwise related to Lindelöf bitopological spaces. Lindelöf spaces are among of the most important topological spaces with important applications in various branches of mathematics. Therefore, many studies on Lindelöf topological spaces and pairwise Lindelöf bitopological spaces were presented in previous papers. However, those two new pairwise Lindelöf bitopological spaces are more general than what has been studied before. Therefore, the study defines a new pairwise interior operator and a new pairwise closure operator, furthermore, it reviews their characteristics where the researchers provide new strongly pairwise axioms (the strongly pairwise regular and the strongly pairwise normal axioms) in bitopological spaces. Moreover, many illustrative examples and counterexamples are reviewed, and a study was conducted on the relationship between the strongly pairwise regular axioms and the pairwise regular axioms, and the relationship between the strongly pairwise normal axioms and the pairwise normal axioms. In addition, this study presents some important results in strongly regular and strongly normal bitopological spaces. Finally, the findings showed some relationships between the new concepts of Lindelöf bitopological spaces.