Computably regular topological spaces
This article continues the study of computable elementary topology started by the author and T. Grubba in 2009 and extends the author's 2010 study of axioms of computable separation. Several computable T3- and Tychonoff separation axioms are introduced and their logical relation is investigated...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2013-08-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/1192/pdf |
| _version_ | 1797268695301488640 |
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| author | Klaus Weihrauch |
| author_facet | Klaus Weihrauch |
| author_sort | Klaus Weihrauch |
| collection | DOAJ |
| description | This article continues the study of computable elementary topology started by
the author and T. Grubba in 2009 and extends the author's 2010 study of axioms
of computable separation. Several computable T3- and Tychonoff separation
axioms are introduced and their logical relation is investigated. A number of
implications between these axioms are proved and several implications are
excluded by counter examples, however, many questions have not yet been
answered. Known results on computable metrization of T3-spaces from M.
Schr/"oder (1998) and T. Grubba, M. Schr/"oder and the author (2007) are proved
under uniform assumptions and with partly simpler proofs, in particular, the
theorem that every computably regular computable topological space with
non-empty base elements can be embedded into a computable metric space. Most of
the computable separation axioms remain true for finite products of spaces. |
| first_indexed | 2024-04-25T01:36:34Z |
| format | Article |
| id | doaj.art-61a79bbfda5e4fd583e0b13e97c04911 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:36:34Z |
| publishDate | 2013-08-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-61a79bbfda5e4fd583e0b13e97c049112024-03-08T09:29:28ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742013-08-01Volume 9, Issue 310.2168/LMCS-9(3:5)20131192Computably regular topological spacesKlaus WeihrauchThis article continues the study of computable elementary topology started by the author and T. Grubba in 2009 and extends the author's 2010 study of axioms of computable separation. Several computable T3- and Tychonoff separation axioms are introduced and their logical relation is investigated. A number of implications between these axioms are proved and several implications are excluded by counter examples, however, many questions have not yet been answered. Known results on computable metrization of T3-spaces from M. Schr/"oder (1998) and T. Grubba, M. Schr/"oder and the author (2007) are proved under uniform assumptions and with partly simpler proofs, in particular, the theorem that every computably regular computable topological space with non-empty base elements can be embedded into a computable metric space. Most of the computable separation axioms remain true for finite products of spaces.https://lmcs.episciences.org/1192/pdfmathematics - logic |
| spellingShingle | Klaus Weihrauch Computably regular topological spaces Logical Methods in Computer Science mathematics - logic |
| title | Computably regular topological spaces |
| title_full | Computably regular topological spaces |
| title_fullStr | Computably regular topological spaces |
| title_full_unstemmed | Computably regular topological spaces |
| title_short | Computably regular topological spaces |
| title_sort | computably regular topological spaces |
| topic | mathematics - logic |
| url | https://lmcs.episciences.org/1192/pdf |
| work_keys_str_mv | AT klausweihrauch computablyregulartopologicalspaces |