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A note on the comparison of topologies. (English) Zbl 0982.54031

Summary: A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom \(\tau S_2\sigma\) which is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly [J. Lond. Math. Soc., II. Ser. 15, 169-172 (1977; Zbl 0348.54025)] regarding the comparison of topologies.

MSC:

54E55 Bitopologies
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

Citations:

Zbl 0348.54025
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