Geodesic
Remarks on star countable discrete closed spaces
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 451-460
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In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) 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.
In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) 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.
DOI : 10.1007/s10587-013-0029-x
Classification : 54D20
Keywords: pseudocompact; normal; Tychonoff; star countable; absolutely star countable; star countable discrete closed; absolutely star countable discrete closed space 
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Song, Yan-Kui. Remarks on star countable discrete closed spaces. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 451-460. doi: 10.1007/s10587-013-0029-x

[1] Aiken, L. P.: Star-covering properties: generalized $\Psi$-spaces, countability conditions, reflection. Topology Appl. 158 (2011), 1732-1737. | DOI | MR | Zbl

[2] Alas, O. T., Junqueira, L. R., Wilson, R. G.: Countability and star covering properties. Topology Appl. 158 (2011), 620-626. | DOI | MR | Zbl

[3] Alas, O. T., Junqueira, L. R., Mill, J. van, Tkachuk, V. V., Wilson, R. G.: On the extent of star countable spaces. Cent. Eur. J. Math. 9 (2011), 603-615. | DOI | MR

[4] Bonanzinga, M.: Star-Lindelöf and absolutely star-Lindelöf spaces. Questions Answers Gen. Topology. 16 (1998), 79-104. | MR | Zbl

[5] Engelking, R.: General Topology. Rev. and compl. ed. Sigma Series in Pure Mathematics 6, Heldermann, Berlin (1989). | MR | Zbl

[6] Matveev, M. V.: Absolutely countably compact spaces. Topology Appl. 58 (1994), 81-92. | DOI | MR | Zbl

[7] Matveev, M. V.: A survey on star-covering properties. Topological Atlas preprint No 330 (1998).

[8] Matveev, M. V.: On space in countable web. arxiv:math/0006199v1 (2000).

[9] Song, Y.-K.: Discretely star-Lindelöf spaces. Tsukuba J. Math. 25 (2001), 371-382. | DOI | MR | Zbl

[10] Song, Y.-K.: Closed subsets of absolutely star-Lindelöf spaces II. Commentat. Math. Univ. Carol. 44 (2003), 329-334. | MR | Zbl

[11] Song, Y.-K.: Remarks on discretely absolutely star-Lindelöf spaces. Czech. Math. J. 58 (2008), 823-831. | DOI | MR

[12] Song, Y.-K.: Remarks on countability and star covering properties. Topology Appl. 158 (2011), 1121-1123. | DOI | MR | Zbl

[13] Tall, F. D.: Normality versus collectionwise normality. Handbook of Set-Theoretic Topology K. Kunen and J. E. Vaughan North-Holland, Amsterdam (1984), 685-732. | MR | Zbl

[14] Douwen, E. K. van, Reed, G. M., Roscoe, A. W., Tree, I. J.: Star covering properties. Topology Appl. 39 (1991), 71-103. | DOI | MR

[15] Mill, J. van, Tkachuk, V. V., Wilson, R. G.: Classes defined by stars and neighbourhood assignments. Topology Appl. 154 (2007), 2127-2134. | DOI | MR

[16] Vaughan, J. E.: On the product of a compact space with an absolutely countably compact space. Ann. N. Y. Acad. Sci. 788 (1996), 203-208. | DOI | MR | Zbl

[17] Yasui, Y., Gao, Z.-M.: Spaces in countable web. Houston J. Math. 25 (1999), 327-335. | MR | Zbl

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