Geodesic
Some properties of relatively strong pseudocompactness
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1145-1152

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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 $Y\subset \overline {{\rm Int} Y}$ 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.
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.
Classification : 54D20, 54D30
Keywords: relative topological properties; pseudocompact spaces; compact space 
Zhang, Guo-Fang. Some properties of relatively strong pseudocompactness. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1145-1152. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a19/
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