REMARKS ON CS-STARCOMPACT SPACES
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A space X is cs-starcompact if for every open cover $\mathcal{U}$ of X, there exists a convergent sequence S of X such that St(S, $\mathcal{U}$) = X, where $St(S,\mathcal{U})\;=\; \cup\{U{\in}\mathcal{U}:U{\cap}S{\neq}\phi\}$. In this paper, we prove the following statements: (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel$\ddot{o}$f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace. (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel{\"o}f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.
Abstract
A space X is cs-starcompact if for every open cover $\mathcal{U}$ of X, there exists a convergent sequence S of X such that St(S, $\mathcal{U}$) = X, where $St(S,\mathcal{U})\;=\; \cup\{U{\in}\mathcal{U}:U{\cap}S{\neq}\phi\}$. In this paper, we prove the following statements: (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel$\ddot{o}$f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace. (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel{\"o}f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.
참고문헌 (10)
- M. Bonanzinga, "Closed subspaces of star-Lindelof and related spaces", East-West J. Math, 2(2), pp.171~179 (2000)
- M. Bonanzinga, "Products of star-Lindelof and related spaces", Houston J. Math, 27(1), pp.45~57 (2001)
- E. K. van Douwn, "Star covering properties", Topology Appl, 39(1), pp.71~103 (1991)
- R. Engelking, "General Topology" (1989), Heldermann Verlag
- W. M. Fleischman, "A new extension of countable compactness", Fund. Math, 67, pp.1~7 (1970)
- M. V. Matveev, "A survey on star-covering properties", Topological Atlas, (330) (1998)
- M. V. Matveev, "How weak is weak extent?", Topology Appl, 119(2), pp.229~232 (2002)
- J. van Mill, "Classes de ned by stars and neighbourhood assignments", Topology Appl, 154(10), pp.2127~2134 (2007)
- Y.-K. Song, "On K-starcompact spaces", Bull. Malays. Math. Sci. Soc, 30(1), pp.59~64 (2007)
- Y.-K. Song, "On countable star-covering properties", Appl. Gen. Topol, 8(2), pp.249~258 (2007)