Yan-Kui Song
Abstract
In this paper, we prove the following statements: (1) There exists a pseudocompact star σ-compact Tychonoff space having a regular-closed subspace which is not star σ -compact. (2) Assuming 2N0 = 2N1 , there exists a star countable (hence star σ-compact) normal space having a regular-closed subspace which is not star σ-compact.
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In this paper, we prove the following statements: (1) There exists a pseudocompact star σ-compact Tychonoff space having a regular-closed subspace which is not star σ -compact. (2) Assuming 2N0 = 2N1 , there exists a star countable (hence star σ-compact) normal space having a regular-closed subspace which is not star σ-compact.
Key concepts: Star (game theory), Subspace topology, Tychonoff space, Countable set, Regular space, Mathematics, Space (punctuation), Relatively compact subspace