Some properties of relatively strong pseudocompactness

Guo-Fang Zhang

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1145-1152
  • ISSN: 0011-4642

Abstract

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In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space X and a subspace Y satisfy that Y ⊂ Int Y ¯ and Y is strongly pseudocompact and metacompact in X , then Y is compact in X . We also give an example to demonstrate that the condition Y ⊂ Int Y ¯ can not be omitted.

How to cite

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Zhang, Guo-Fang. "Some properties of relatively strong pseudocompactness." Czechoslovak Mathematical Journal 58.4 (2008): 1145-1152. <http://eudml.org/doc/37892>.

@article{Zhang2008,
abstract = {In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space $X$ and a subspace $Y$ satisfy that $Y\subset \overline\{\{\rm Int\} Y\}$ and $Y$ is strongly pseudocompact and metacompact in $X$, then $Y$ is compact in $X$. We also give an example to demonstrate that the condition $Y\subset \overline\{\{\rm Int\} Y\}$ can not be omitted.},
author = {Zhang, Guo-Fang},
journal = {Czechoslovak Mathematical Journal},
keywords = {relative topological properties; pseudocompact spaces; compact space; relative topological properties; pseudocompact spaces; compact space},
language = {eng},
number = {4},
pages = {1145-1152},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some properties of relatively strong pseudocompactness},
url = {http://eudml.org/doc/37892},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Zhang, Guo-Fang
TI - Some properties of relatively strong pseudocompactness
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1145
EP - 1152
AB - In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space $X$ and a subspace $Y$ satisfy that $Y\subset \overline{{\rm Int} Y}$ and $Y$ is strongly pseudocompact and metacompact in $X$, then $Y$ is compact in $X$. We also give an example to demonstrate that the condition $Y\subset \overline{{\rm Int} Y}$ can not be omitted.
LA - eng
KW - relative topological properties; pseudocompact spaces; compact space; relative topological properties; pseudocompact spaces; compact space
UR - http://eudml.org/doc/37892
ER -

References

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  1. Arhangel'skii, A. V., From classic topological invariant to relative topological properties, Sci. Math. Japon. 55 (2001), 153-201. (2001) MR1885790
  2. Arhangel'skii, A. V., Location type properties: relative strong pseudocompactness, Trudy Matem. Inst. RAN 193 (1992), 28-30. (1992) 
  3. Arhangel'skii, A. V., Genedi, H. M. M., Beginning of the theory of relative topological properties, General Topology: Space and Mapping MGU Moscow (1989), 3-48 Russian. (1989) 
  4. Engelking, R., General Topology. Sigma Series in Pure Mathematics, Heldermann Berlin (1989). (1989) MR1039321
  5. Grabner, E. M., Grabnor, G. C., Miyazaki, K., On properties of relative metacompactness and paracompactness type, Topol. Proc. 25 (2000), 145-177. (2000) MR1925682
  6. Scott, B. M., Pseudocompact metacompact spaces are compact, Topology, Proc. Conf. 4 (1979), 577-587. (1979) MR0598295

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