Weak continuity and strongly closed sets
After demonstrating the usual product theorems for weakly continuous functions, strongly closed and extremely closed subsets are contrasted to support the conjecture that a product of faintly continuous functions need not be faintly continuous. Strongly closed sets are used to characterize Hausdorff...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000831 |
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doaj-05edd5f8575b499aa3371819bc67fe2b2020-11-24T23:15:53ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017480981610.1155/S0161171284000831Weak continuity and strongly closed setsD. A. Rose0Department of Mathemtics, Francis Marion College, Florence 29501, South Carolina , USAAfter demonstrating the usual product theorems for weakly continuous functions, strongly closed and extremely closed subsets are contrasted to support the conjecture that a product of faintly continuous functions need not be faintly continuous. Strongly closed sets are used to characterize Hausdorff spaces and Urysohn spaces, and with these characterizations two results obtained by T. Noiri are obtained by function-theoretic means rather than by point-set method.http://dx.doi.org/10.1155/S0161171284000831weak continuityfaint continuitysubweak continuitystrongly closed sets. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
D. A. Rose |
| spellingShingle |
D. A. Rose Weak continuity and strongly closed sets International Journal of Mathematics and Mathematical Sciences weak continuity faint continuity subweak continuity strongly closed sets. |
| author_facet |
D. A. Rose |
| author_sort |
D. A. Rose |
| title |
Weak continuity and strongly closed sets |
| title_short |
Weak continuity and strongly closed sets |
| title_full |
Weak continuity and strongly closed sets |
| title_fullStr |
Weak continuity and strongly closed sets |
| title_full_unstemmed |
Weak continuity and strongly closed sets |
| title_sort |
weak continuity and strongly closed sets |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1984-01-01 |
| description |
After demonstrating the usual product theorems for weakly continuous functions, strongly closed and extremely closed subsets are contrasted to support the conjecture that a product of faintly continuous functions need not be faintly continuous. Strongly closed sets are used to characterize Hausdorff spaces and Urysohn spaces, and with these characterizations two results obtained by T. Noiri are obtained by function-theoretic means rather than by point-set method. |
| topic |
weak continuity faint continuity subweak continuity strongly closed sets. |
| url |
http://dx.doi.org/10.1155/S0161171284000831 |
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AT darose weakcontinuityandstronglyclosedsets |
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