Exercise 2.1.11 (Kuratowski's closure-complement problem)

Question

Prove the following result, \href{http://matwbn.icm.edu.pl/ksiazki/fm/fm3/fm3121.pdf}{originally noted by Kuratowski}: If $S$ is a subset of a topological space $X$, then there are at most $14$ subsets of $X$ that can be obtained from $S$ by successively taking either complements or closures. Find a subset $S$ of $U$ such that exactly fourteen subsets of $\mathbb{R}$ can be obtained from $S$ in this manner.

Elu Thingol · Accepted Answer

See \href{https://math.solverer.com/library/james_munkres/topology_classic_version/exercise_17-21}{this answer}.

Exercise 2.1.11 (Kuratowski's closure-complement problem)

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Exercise 2.1.11 (Kuratowski's closure-complement problem)

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