# Does the interior of a Kuratowski 14-set in a finite space always have cardinality 1?

A subset A of a topological space X is called a Kuratowski 14-set if exactly 14 different sets (including A) can be obtained from A by alternately taking closures and complements.

Let $c$ denote complement and $i$ interior: If $X$ is finite and $A$ is a Kuratowski 14 set, is it always true that $|A^{i}|=|A^{ci}|=1$?

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