Let $X$ be a non-Hausdorff compact topological space, and $A\subseteq X$ be an infinite subset of $X $, such that $a\in \overline{A-\{a\}}$ for every $a\in A $, where $\overline{A-\{a\}}$ is the closure of $A-\{a\}$ in $X$. Is there any equivalent condition for this property of $A$.