My Math Forum open and close set

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 February 17th, 2013, 05:31 AM #1 Newbie   Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0 open and close set if the union of open and close set is open? And the intesection is closed? How?
 February 17th, 2013, 05:39 AM #2 Newbie   Joined: Feb 2012 Posts: 28 Thanks: 0 Re: open and close set Take the set $A= \{x \in \mathbb{R} | 0 < x=< 5\}=$ and the set $B= \{y \in \mathbb{R} | 2 \leq y \leq 4\}$. We have that $A \cup B= \{x \in \mathbb{R} | 0 < x=< 5\}=$ so $A \cup B$ is an open set. Observe that $A \cap B= \{x \in \mathbb{R} | 2 \leq x \leq 4\}$ so $A \cap B$ is a closed set. Intuitively you can think of it this way: taking the union of two sets means that you have to include all points in both sets in the union of the sets. Taking the intersection means that you only take the points that are in both sets. So, if $B$ is a closed set and is a subset of $A$ then $A \cap B= B$ so $A \cap B$ is a closed set.

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