# Open sets and closed sets

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• February 11th 2010, 06:43 PM
Slazenger3
Open sets and closed sets
Explain why, if U is open and H is closed, then the set U \ H must be open.
• February 11th 2010, 06:57 PM
Drexel28
Quote:

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!