Compact-calibres of regular and monotonically normal spaces
A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set wh...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011365 |
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| _version_ | 1849398983067172864 |
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| author | David W. Mcintyre |
| author_facet | David W. Mcintyre |
| author_sort | David W. Mcintyre |
| collection | DOAJ |
| description | A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp.,
point-finite) collection of nonempty open sets is countable. It
has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every disjoint (resp., discrete) collection of
nonempty open sets is countable. The relative strengths of these six conditions are determined for Moore spaces, regular first countable spaces, linearly-ordered spaces, and arbitrary regular spaces. It is shown that the relative strengths for spaces with point-countable bases are the same as those for Moore spaces, and the relative strengths for linearly-ordered spaces are the same
as those for arbitrary monotonically normal spaces. |
| format | Article |
| id | doaj-art-a406efa3a5234b3c8e36e4b96654d99c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a406efa3a5234b3c8e36e4b96654d99c2025-08-20T03:38:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129420921610.1155/S0161171202011365Compact-calibres of regular and monotonically normal spacesDavid W. Mcintyre0Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New ZealandA topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every disjoint (resp., discrete) collection of nonempty open sets is countable. The relative strengths of these six conditions are determined for Moore spaces, regular first countable spaces, linearly-ordered spaces, and arbitrary regular spaces. It is shown that the relative strengths for spaces with point-countable bases are the same as those for Moore spaces, and the relative strengths for linearly-ordered spaces are the same as those for arbitrary monotonically normal spaces.http://dx.doi.org/10.1155/S0161171202011365 |
| spellingShingle | David W. Mcintyre Compact-calibres of regular and monotonically normal spaces International Journal of Mathematics and Mathematical Sciences |
| title | Compact-calibres of regular and monotonically normal spaces |
| title_full | Compact-calibres of regular and monotonically normal spaces |
| title_fullStr | Compact-calibres of regular and monotonically normal spaces |
| title_full_unstemmed | Compact-calibres of regular and monotonically normal spaces |
| title_short | Compact-calibres of regular and monotonically normal spaces |
| title_sort | compact calibres of regular and monotonically normal spaces |
| url | http://dx.doi.org/10.1155/S0161171202011365 |
| work_keys_str_mv | AT davidwmcintyre compactcalibresofregularandmonotonicallynormalspaces |