Remarks on star countable discrete closed spaces |
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Authors: | Yan-Kui Song |
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Institution: | 1. Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing, 210046, P. R. China
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Abstract: | In this paper, we prove the following statements: - There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable.
- Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace.
- Assuming $2^{\aleph _0 } = 2^{\aleph _1 } $ , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.
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