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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |