Let A and B be subsets of with , denoting the sets of interior points for A and B respectively. Prove that is a subset of the interior of AUB. Give an example where the inclusion is strict.

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- Sep 14th 2010, 03:16 PMwopashuiinterior points question
Let A and B be subsets of with , denoting the sets of interior points for A and B respectively. Prove that is a subset of the interior of AUB. Give an example where the inclusion is strict.

- Sep 15th 2010, 03:35 AMHallsofIvy
One reason we ask people to show there work is that there are a number of different ways of defining "interior points" and without seeing what you are trying we don't know which is appropriate for you. I suspect you are using "p is an interior point of p if and only if there exist a neighborhood of p that is a subset of A".

So if p is in then it is in both and . Since it is in there exist some neighborhood of p, ( is the radius), such that . Since p is in , there exist some neighborhood of p, such that .

Can you finish now? - Sep 15th 2010, 04:08 AMlvleph
@HallsofIvy

If . It is not necessary for that case would be necessary for the intersection not union. - Sep 15th 2010, 05:11 AMMathoMan
- Sep 15th 2010, 07:56 AMHallsofIvy