• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.569-573
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• 2007

In this note, we construct an example of a Hausdorff K-starcompact (hence, $1\frac{1}{2}$-star-compact) space X having a regular closed $G_{\delta}-subset$ which is not $1\frac{1}{2}$-starcompact (hence, not K-starcompact).

• Honam Mathematical Journal
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• v.24 no.1
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• pp.131-142
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• 2002

A $1{\frac{1}{2}}$-starcompact space has one of the most curious properties among the spaces of starcompactness. It is not too far away from countably compact spaces and may be considered as the first candidate for extending theorems about countably compact spaces. Unfortunately, $1{\frac{1}{2}}$-starcompactness is not so easy to be recognized as 2-starcompactness which will follow from countable pracompactness. We investigate some properties around $1{\frac{1}{2}}$-starcompact spaces.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.201-205
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• 2012

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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.723-731
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• 2003

In this paper, we study topological operations of iterated star covering properties, i.e., subspaces, products, and images and preimages of iterated starcompact spaces.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.453-465
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• 2010

In this paper, we consider countable version of star covering properties to get interesting results about the relationship between starcompactness and countable pracompactness. We also construct examples related to countable pracompactness and H-closedness.

• Honam Mathematical Journal
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• v.26 no.2
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• pp.193-208
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• 2004

In this paper, we further enrich the theory of starcompactness properties by clarifying relationships between various types of weak covering properties and starcompactness and starcompactness-like properties. We also study star-$Linde{\ddot{o}}fness$ of ${\sigma}$-product spaces.