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Keywords:
Aull-paracompactness of $Y$ in $X$; strong star-normality of $Y$ in $X$
Aull-paracompactness of $Y$ in $X$; strong star-normality of $Y$ in $X$
Summary:
We prove for a subspace $Y$ of a $T_1$-space $X$, $Y$ is (strictly) Aull-paracompact in $X$ and $Y$ is Hausdorff in $X$ if and only if $Y$ is strongly star-normal in $X$. This result provides affirmative answers to questions of A.V. Arhangel'skii–I.Ju. Gordienko [3] and of A.V. Arhangel'skii [2].
References:
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