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A topological space $X$ is called relative extremely disconnected if it has a base $B$ (for open subsets) such that disjoint elements in $B$ have disjoint closure. Does it exist an infinite Hausdorff space $X$ which is not relative extremely disconnected?

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A topological space $X$ is called relative extremely disconnected if it has a base $B$ (for open subsets) such that disjoint elements in $B$ have disjoint closure. Does exist infinite Hausdorff space $X$ which is not relative extremely disconnected?

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# Relative extremely disconnected space

A topological space $X$ is called relative extremely disconnected if it has a base $B$ (for open subsets) such that disjoint elements in $B$ have disjoint closure. Does exist Hausdorff space $X$ which is not relative extremely disconnected?