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February 17th, 2013, 05:31 AM   #1
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open and close set

if the union of open and close set is open?
And the intesection is closed?
How?
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February 17th, 2013, 05:39 AM   #2
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Re: open and close set

Take the set and the set . We have that so is an open set. Observe that so 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 is a closed set and is a subset of then so is a closed set.
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