# Sets

• November 12th 2009, 04:16 PM
p00ndawg
Sets
Let S and T be subsets of R. Prove the Following:

A) int(int S) = int S

for this one do I just need to take the set S, and show that the interiors interior is still part of the interior?

B) int(S $\cap$ T) = (int S) $\cap$ (int T)

For this one do I just assume there is some x $\in$ int(S $\cap$ T) and follow from there?
• November 12th 2009, 04:37 PM
Plato
This is all about open sets.
The interior of a set is an open set: it is the union of open sets.
So surely $\text{int}(\text{int}(S))=\text{int}(S)$
• November 12th 2009, 04:42 PM
p00ndawg
Quote:

Originally Posted by Plato
This is all about open sets.
The interior of a set is an open set: it is the union of open sets.
So surely $\text{int}(\text{int}(S))=\text{int}(S)$

ohh i see.

I have a whole section with questions similar to these for homework.
I wasnt quite sure how to approach them.

thanks