🇨🇦 Math prof at UNBC. Former Chair of Mathematics & Statistics Dept (Mar 2016 - Jun 2020). Presbyterian Christian.
Jul 7, 2019 • 4 tweets • 3 min read
For any subset A of a topological space X, there are no more than 14 sets that can be formed from A using the closure and complement operations. The complement of B is B' = X-B. Closure C(B) = smallest closed set containing B. (Neat problem from Kelley's General #Topology.) #math
There's a lemma that helps one show this. Letting C(A) denote the closure of A, and N(A) the complement of A, we can prove:
Lemma: for all sets A, one has the equation
CNC N CNC(A) = CNC(A).
