Monotone normality in products
Monotone normality in finite and infinite topological products is investigated. As shown in (Heath et al., 1973), the countable (Tychonoff) power of a space is monotonically normal if and only if the space is stratifiable. It is shown that if the square of a space is monotonically normal, then all f...
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| Materyal Türü: | Journal article |
| Dil: | English |
| Baskı/Yayın Bilgisi: |
Elsevier
1999
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| Konular: |
| _version_ | 1826283161021054976 |
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| author | Gartside, P |
| author_facet | Gartside, P |
| author_sort | Gartside, P |
| collection | OXFORD |
| description | Monotone normality in finite and infinite topological products is investigated. As shown in (Heath et al., 1973), the countable (Tychonoff) power of a space is monotonically normal if and only if the space is stratifiable. It is shown that if the square of a space is monotonically normal, then all finite powers are monotonically normal and hereditarily paracompact. For certain special cases, it is observed that a space has all finite powers monotonically normal if and only if it linearly stratifiable. Nonetheless, a monotonically normal topological group is constructed, all of whose finite powers are monotonically normal, but which is not linearly stratifiable. The group is constructed using special filters and nonstandard topologies on infinite products. |
| first_indexed | 2024-03-07T00:54:44Z |
| format | Journal article |
| id | oxford-uuid:87a54830-957a-4fb2-a6a0-279ea788b408 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:54:44Z |
| publishDate | 1999 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:87a54830-957a-4fb2-a6a0-279ea788b4082022-03-26T22:12:06ZMonotone normality in productsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:87a54830-957a-4fb2-a6a0-279ea788b408Analytic Topology or TopologyEnglishOxford University Research Archive - ValetElsevier1999Gartside, PMonotone normality in finite and infinite topological products is investigated. As shown in (Heath et al., 1973), the countable (Tychonoff) power of a space is monotonically normal if and only if the space is stratifiable. It is shown that if the square of a space is monotonically normal, then all finite powers are monotonically normal and hereditarily paracompact. For certain special cases, it is observed that a space has all finite powers monotonically normal if and only if it linearly stratifiable. Nonetheless, a monotonically normal topological group is constructed, all of whose finite powers are monotonically normal, but which is not linearly stratifiable. The group is constructed using special filters and nonstandard topologies on infinite products. |
| spellingShingle | Analytic Topology or Topology Gartside, P Monotone normality in products |
| title | Monotone normality in products |
| title_full | Monotone normality in products |
| title_fullStr | Monotone normality in products |
| title_full_unstemmed | Monotone normality in products |
| title_short | Monotone normality in products |
| title_sort | monotone normality in products |
| topic | Analytic Topology or Topology |
| work_keys_str_mv | AT gartsidep monotonenormalityinproducts |