Kuratowski's Closure-Complement Principle

Kuratowski's Closure-Complement Principle is a fundamental idea in topology describing how certain operations—taking the closure of a set and its complement—interact. It states that applying the closure operation twice yields the same result as applying it once, and similarly, the complement operation reverses these effects systematically. Specifically, the sets generated by repeatedly applying closure and complement to any subset of a topological space follow a predictable pattern, with at most 14 distinct sets. This principle helps us understand the structure of closed and open sets within a space, providing a foundation for analyzing topological properties through these operations.