Abstract: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].
Keywords: Aull-paracompactness of $Y$ in $X$, strong star-normality of $Y$ in $X$
AMS Subject Classification: 54D20, 54B05