# Does this weak distinguishing relation among sets have a name?

Sets $A$ and $B$ in a topological space are [name?] if and only if there exists a nonempty open set $E$ such that $E\subset A$ and $E\cap B=\emptyset$.

Since $A$ and $B$ need not be disjoint, modifications of the word "separated" seem inappropriate. Perhaps the condition above is equivalent to some standard relation among sets in a topological space?

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It's equivalent to $A \cap (X-B)$ containing an open set, if that counts as a "standard relation among sets in a topological space." (X is the ambient topological space.) –  only Sep 30 '12 at 16:22
Rather: $A\setminus B$ has nonempty interior. Or: $A^\circ\setminus \bar B$ is not empty. –  Hagen von Eitzen Sep 30 '12 at 16:25
Thank you. There probably is no single word used yet. Just wanted to check first before naming the property myself. –  mathematrucker Sep 30 '12 at 16:41