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relative topological properties; pseudocompact spaces; compact space
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.
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