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A note on the comparison of topologies

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  • Martin M. Kovár

Abstract

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 τ S 2 σ 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 (1977) regarding the comparison of topologies.

Suggested Citation

  • Martin M. Kovár, 2001. "A note on the comparison of topologies," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 26, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:242197
    DOI: 10.1155/S0161171201005518
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