Given an open set A, and a closed set B.
Is the union, $A\cup B$ also closed?
I’m not too sure how to prove/disprove this statement. Any help would be appreciated.
(I’ve seen a similar question but that looked like it required some topology knowledge; I’m solving this problem from the point of view of someone taking introductory real analysis)
Best Answer
Not necessarily. Take $A = [-1, 1]$ and $B = (-2, 2)$. Then $A \cup B = (-2, 2)$ which is an open set.