On Semicompact Sets and Associated Properties
We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study several properties of su...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/465387 |
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| author | Mohammad S. Sarsak |
| author_facet | Mohammad S. Sarsak |
| author_sort | Mohammad S. Sarsak |
| collection | DOAJ |
| description | We continue the study of semicompact sets in a topological space. Several
properties, mapping properties of semicompact sets are studied.
A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if
every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study
several properties of such spaces, it is mainly shown that a semi-𝑇2 semicompact space is 𝑆𝐶𝑆 if and only if it is extremally disconnected.
It is also shown that in an 𝑜𝑠-regular space 𝑋 if every point has an 𝑆𝐶𝑆 neighborhood, then 𝑋 is 𝑆𝐶𝑆. |
| format | Article |
| id | doaj-art-01e1a2d5dc2b44fdaeef22c0f8d50d78 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-01e1a2d5dc2b44fdaeef22c0f8d50d782025-08-20T02:01:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/465387465387On Semicompact Sets and Associated PropertiesMohammad S. Sarsak0Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 150459, Zarqa 13115, JordanWe continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study several properties of such spaces, it is mainly shown that a semi-𝑇2 semicompact space is 𝑆𝐶𝑆 if and only if it is extremally disconnected. It is also shown that in an 𝑜𝑠-regular space 𝑋 if every point has an 𝑆𝐶𝑆 neighborhood, then 𝑋 is 𝑆𝐶𝑆.http://dx.doi.org/10.1155/2009/465387 |
| spellingShingle | Mohammad S. Sarsak On Semicompact Sets and Associated Properties International Journal of Mathematics and Mathematical Sciences |
| title | On Semicompact Sets and Associated Properties |
| title_full | On Semicompact Sets and Associated Properties |
| title_fullStr | On Semicompact Sets and Associated Properties |
| title_full_unstemmed | On Semicompact Sets and Associated Properties |
| title_short | On Semicompact Sets and Associated Properties |
| title_sort | on semicompact sets and associated properties |
| url | http://dx.doi.org/10.1155/2009/465387 |
| work_keys_str_mv | AT mohammadssarsak onsemicompactsetsandassociatedproperties |