Geodesic
On relatively almost countably compact subsets
Mathematica Bohemica, Tome 135 (2010) no. 3, pp. 291-297

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MR Zbl
A subset $Y$ of a space $X$ is almost countably compact in $X$ if for every countable cover $\Cal U$ of $Y$ by open subsets of $X$, there exists a finite subfamily $\Cal V$ of $\Cal U$ such that $Y\subseteq \overline {\bigcup \Cal V}$. In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets.
A subset $Y$ of a space $X$ is almost countably compact in $X$ if for every countable cover $\Cal U$ of $Y$ by open subsets of $X$, there exists a finite subfamily $\Cal V$ of $\Cal U$ such that $Y\subseteq \overline {\bigcup \Cal V}$. In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets.
DOI : 10.21136/MB.2010.140705
Classification : 54D15, 54D20
Keywords: countably compact space; almost countably compact space; relatively almost countably compact subset 
Song, Yan-Kui; Zheng, Shu-Nian. On relatively almost countably compact subsets. Mathematica Bohemica, Tome 135 (2010) no. 3, pp. 291-297. doi: 10.21136/MB.2010.140705
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[1] Bonanzinga, M., Matveev, M. V., Pareek, C. M.: Some remarks on generalizations of countably compact spaces and Lindelöf spaces. Rend. Circ. Mat. Palermo (2) 51 (2002), 163-174. | DOI | MR | Zbl

[2] Engelking, R.: General Topology. Heldermann Berlin (1989). | MR | Zbl

[3] Mashhour, A. S., El-Monsef, M. E. Abd, El-Deeb, S. N.: On precontinuous and weak precontinuous mappings. Proc. Math. Phys. Soc. Egypt 53 (1983), 47-53. | MR

[4] Sarsak, M. S.: On relatively almost Lindelöf subsets. Acta Math. Hungar 97 (2002), 109-114. | DOI | MR | Zbl

[5] Song, Y.-K.: On almost countably compact spaces. Preprint.

[6] Wilansky, A.: Topics in Functional Analysis. Springer Berlin (1967). | MR | Zbl

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