# Article

 Title: Some properties of relatively strong pseudocompactness (English) Author: Zhang, Guo-Fang Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 58 Issue: 4 Year: 2008 Pages: 1145-1152 Summary lang: English . Category: math . Summary: 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. (English) Keyword: relative topological properties Keyword: pseudocompact spaces Keyword: compact space MSC: 54D20 MSC: 54D30 idZBL: Zbl 1174.54016 idMR: MR2471172 . Date available: 2010-07-21T08:13:18Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/140446 . Reference: [1] Arhangel'skii, A. V.: From classic topological invariant to relative topological properties.Sci. Math. Japon. 55 (2001), 153-201. MR 1885790 Reference: [2] Arhangel'skii, A. V.: Location type properties: relative strong pseudocompactness.Trudy Matem. Inst. RAN 193 (1992), 28-30. Reference: [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. Reference: [4] Engelking, R.: General Topology. Sigma Series in Pure Mathematics.Heldermann Berlin (1989). MR 1039321 Reference: [5] Grabner, E. M., Grabnor, G. C., Miyazaki, K.: On properties of relative metacompactness and paracompactness type.Topol. Proc. 25 (2000), 145-177. MR 1925682 Reference: [6] Scott, B. M.: Pseudocompact metacompact spaces are compact.Topology, Proc. Conf. 4 (1979), 577-587. MR 0598295 .

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