A note on the comparison of topologies
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...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005518 |
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| _version_ | 1832559938524676096 |
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| author | Martin M. Kovár |
| author_facet | Martin M. Kovár |
| author_sort | Martin M. Kovár |
| collection | DOAJ |
| description | 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 τS2σ 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. |
| format | Article |
| id | doaj-art-e6938b05b21446f3bcd5e0c9becc7cb3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e6938b05b21446f3bcd5e0c9becc7cb32025-02-03T01:28:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126423323710.1155/S0161171201005518A note on the comparison of topologiesMartin M. Kovár0Department of Mathematics, Faculty of Electrical Engineering and Computer Science, Technical University of Brno, Technická 8, Brno 616 69, Czech RepublicA 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 τS2σ 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.http://dx.doi.org/10.1155/S0161171201005518 |
| spellingShingle | Martin M. Kovár A note on the comparison of topologies International Journal of Mathematics and Mathematical Sciences |
| title | A note on the comparison of topologies |
| title_full | A note on the comparison of topologies |
| title_fullStr | A note on the comparison of topologies |
| title_full_unstemmed | A note on the comparison of topologies |
| title_short | A note on the comparison of topologies |
| title_sort | note on the comparison of topologies |
| url | http://dx.doi.org/10.1155/S0161171201005518 |
| work_keys_str_mv | AT martinmkovar anoteonthecomparisonoftopologies AT martinmkovar noteonthecomparisonoftopologies |