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The main idea of this research is to consider fibrewise pairwise versions of the more important separation axioms of ordinary bitopology named 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 it.2010 MSC: 55R70, 54C05,54C08,54C10, 54D10, 54D15.
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