# Thread: Open sets and closed sets

1. ## Open sets and closed sets

Explain why, if U is open and H is closed, then the set U \ H must be open.

2. Originally Posted by Slazenger3
Explain why, if U is open and H is closed, then the set U \ H must be open.
Because, whatever definition of open you're using we have that $H$ is closed means $H'$ is open, and so $U-H=U\cap H'$ which is the intersection of two open sets...which is...open!