A Study of Some Generalizations of Fibrewise Bitopological Spaces

In this research, we introduce a study about bitopological space in fibrewise sets. We generalize some fundamental results from fibrewise topology into fibrewise bitopological space. We also introduce the concepts of fibrewise closed bitopological spaces, fibrewise open bitopological spaces, fibrewise locally sliceable bitopological spaces, and fibrewise locally sectionable bitopological spaces. We state and prove several propositions concerning with these concepts. On the other hand, we extend separation axioms of ordinary bitopology into fibrewise setting. The separation axioms we extend are called fibrewise pairwise bi-T_0 spaces, fibrewise pairwise bi -T_1 spaces, fibrewise pairwise bi-R_0 spaces, fibrewise pairwise bi-Hausdorff spaces, fibrewise pairwise functionally bi-Hausdorff spaces, fibrewise pairwise bi-regular spaces, fibrewise pairwise completely bi-regular spaces, fibrewise pairwise bi-normal spaces, and fibrewise pairwise functionally bi-normal spaces. In addition, we offer some results concerning these extended axioms.