On relatively almost countably compact subsets

Yan-Kui Song; Shu-Nian Zheng

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 3, page 291-297
  • ISSN: 0862-7959

Abstract

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A subset Y of a space X is almost countably compact in X if for every countable cover 𝒰 of Y by open subsets of X , there exists a finite subfamily 𝒱 of 𝒰 such that Y 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.

How to cite

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Song, Yan-Kui, and Zheng, Shu-Nian. "On relatively almost countably compact subsets." Mathematica Bohemica 135.3 (2010): 291-297. <http://eudml.org/doc/38131>.

@article{Song2010,
abstract = {A subset $Y$ of a space $X$ is almost countably compact in $X$ if for every countable cover $\mathcal \{U\}$ of $Y$ by open subsets of $X$, there exists a finite subfamily $\mathcal \{V\}$ of $\mathcal \{U\}$ such that $Y\subseteq \overline\{\bigcup \mathcal \{V\}\}$. 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.},
author = {Song, Yan-Kui, Zheng, Shu-Nian},
journal = {Mathematica Bohemica},
keywords = {countably compact space; almost countably compact space; relatively almost countably compact subset; countably compact space; almost countably compact space; relatively almost countably compact subset},
language = {eng},
number = {3},
pages = {291-297},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On relatively almost countably compact subsets},
url = {http://eudml.org/doc/38131},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Song, Yan-Kui
AU - Zheng, Shu-Nian
TI - On relatively almost countably compact subsets
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 3
SP - 291
EP - 297
AB - A subset $Y$ of a space $X$ is almost countably compact in $X$ if for every countable cover $\mathcal {U}$ of $Y$ by open subsets of $X$, there exists a finite subfamily $\mathcal {V}$ of $\mathcal {U}$ such that $Y\subseteq \overline{\bigcup \mathcal {V}}$. 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.
LA - eng
KW - countably compact space; almost countably compact space; relatively almost countably compact subset; countably compact space; almost countably compact space; relatively almost countably compact subset
UR - http://eudml.org/doc/38131
ER -

References

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  1. Bonanzinga, M., Matveev, M. V., Pareek, C. M., 10.1007/BF02871459, Rend. Circ. Mat. Palermo (2) 51 (2002), 163-174. (2002) Zbl1194.54008MR1905715DOI10.1007/BF02871459
  2. Engelking, R., General Topology, Heldermann Berlin (1989). (1989) Zbl0684.54001MR1039321
  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. (1983) MR0830896
  4. Sarsak, M. S., 10.1023/A:1020811012865, Acta Math. Hungar 97 (2002), 109-114. (2002) Zbl1006.54030MR1932797DOI10.1023/A:1020811012865
  5. Song, Y.-K., On almost countably compact spaces, Preprint. 
  6. Wilansky, A., Topics in Functional Analysis, Springer Berlin (1967). (1967) Zbl0156.36103MR0223854

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