Compact and extremally disconnected spaces
Viglino defined a Hausdorff topological space to be C-compact if each closed subset of the space is an H-set in the sense of Veličko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is an S-set in the sense of Dickman and Krystock. Such spa...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204208249 |
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| _version_ | 1832552367534374912 |
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| author | Bhamini M. P. Nayar |
| author_facet | Bhamini M. P. Nayar |
| author_sort | Bhamini M. P. Nayar |
| collection | DOAJ |
| description | Viglino defined a Hausdorff topological space to be C-compact
if each closed subset of the space is an H-set in the sense of
Veličko. In this paper, we study the class of Hausdorff spaces
characterized by the property that each closed subset is an
S-set in the sense of Dickman and Krystock. Such spaces are
called C-s-compact. Recently, the notion of strongly
subclosed relation, introduced by Joseph, has been utilized to
characterize C-compact spaces as those with the property that
each function from the space to a Hausdorff space with a strongly
subclosed inverse is closed. Here, it is shown that
C-s-compact spaces are characterized by the property that
each function from the space to a Hausdorff space with a strongly
sub-semiclosed inverse is a closed function. It is established
that this class of spaces is the same as the class of Hausdorff,
compact, and extremally disconnected spaces. The class of
C-s-compact spaces is properly contained in the class of
C-compact spaces as well as in the class of S-closed spaces
of Thompson. In general, a compact space need not be
C-s-compact. The product of two C-s-compact spaces need
not be C-s-compact. |
| format | Article |
| id | doaj-art-842748ba5c2a4a98a742bd1735bdb93b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-842748ba5c2a4a98a742bd1735bdb93b2025-02-03T05:58:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004201047105610.1155/S0161171204208249Compact and extremally disconnected spacesBhamini M. P. Nayar0Department of Mathematics, Morgan State University, Baltimore, MD 21251, USAViglino defined a Hausdorff topological space to be C-compact if each closed subset of the space is an H-set in the sense of Veličko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is an S-set in the sense of Dickman and Krystock. Such spaces are called C-s-compact. Recently, the notion of strongly subclosed relation, introduced by Joseph, has been utilized to characterize C-compact spaces as those with the property that each function from the space to a Hausdorff space with a strongly subclosed inverse is closed. Here, it is shown that C-s-compact spaces are characterized by the property that each function from the space to a Hausdorff space with a strongly sub-semiclosed inverse is a closed function. It is established that this class of spaces is the same as the class of Hausdorff, compact, and extremally disconnected spaces. The class of C-s-compact spaces is properly contained in the class of C-compact spaces as well as in the class of S-closed spaces of Thompson. In general, a compact space need not be C-s-compact. The product of two C-s-compact spaces need not be C-s-compact.http://dx.doi.org/10.1155/S0161171204208249 |
| spellingShingle | Bhamini M. P. Nayar Compact and extremally disconnected spaces International Journal of Mathematics and Mathematical Sciences |
| title | Compact and extremally disconnected spaces |
| title_full | Compact and extremally disconnected spaces |
| title_fullStr | Compact and extremally disconnected spaces |
| title_full_unstemmed | Compact and extremally disconnected spaces |
| title_short | Compact and extremally disconnected spaces |
| title_sort | compact and extremally disconnected spaces |
| url | http://dx.doi.org/10.1155/S0161171204208249 |
| work_keys_str_mv | AT bhaminimpnayar compactandextremallydisconnectedspaces |