Countably I-Compact Spaces
We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is cou...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005889 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850159048049033216 |
|---|---|
| author | Bassam Al-Nashef |
| author_facet | Bassam Al-Nashef |
| author_sort | Bassam Al-Nashef |
| collection | DOAJ |
| description | We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other characterizations are given in terms of covers by semiopen subsets and other types of subsets. We also show that countable I-compactness is invariant under almost open semi-continuous surjections. |
| format | Article |
| id | doaj-art-5fea105232ae40b9ab8d3eb316107f32 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5fea105232ae40b9ab8d3eb316107f322025-08-20T02:23:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01261274575110.1155/S0161171201005889Countably I-Compact SpacesBassam Al-Nashef0Mathematics Department, Yarmouk University, Irbid, JordanWe introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other characterizations are given in terms of covers by semiopen subsets and other types of subsets. We also show that countable I-compactness is invariant under almost open semi-continuous surjections.http://dx.doi.org/10.1155/S0161171201005889 |
| spellingShingle | Bassam Al-Nashef Countably I-Compact Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Countably I-Compact Spaces |
| title_full | Countably I-Compact Spaces |
| title_fullStr | Countably I-Compact Spaces |
| title_full_unstemmed | Countably I-Compact Spaces |
| title_short | Countably I-Compact Spaces |
| title_sort | countably i compact spaces |
| url | http://dx.doi.org/10.1155/S0161171201005889 |
| work_keys_str_mv | AT bassamalnashef countablyicompactspaces |