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 $|A^{i}|=|A^{ci}|=1$?
More generally: if $X$ is any topological space and $A$ is a finite Kuratowski 14-set, is always true that $|A^{i}|$ and $|A^{ci}| are equal to 1?
EDIT: The asnwer is affirmative only when $|X|=7$. What if we relax the condition and request that only one of $|A^{i}|$ or $|A^{ci}|$ is equal to 1?
(There is a related question)