# Thread: Interior and Closure for TOPOLGY

1. ## Interior and Closure for TOPOLGY

I am have run into a problem where I am supposed to prove that for any set A, the boundary of A is a closed set and that for any set A, the boundary of A is a subset of A closure.

2. ## Re: Interior and Closure for TOPOLGY

Originally Posted by kaptain483
I am have run into a problem where I am supposed to prove that for any set A, the boundary of A is a closed set and that for any set A, the boundary of A is a subset of A closure.

Let $A^o,~\beta(A),~\&~\mathcal{E}(A)$ stand for interior, boundary, and exterior of the set $A$.

Now you use basic definitions show those are pair-wise disjoint sets.
If you can do that, then this question is obviously true.

3. ## Re: Interior and Closure for TOPOLGY

how do you show that they are pair wise disjoint sets

4. ## Re: Interior and Closure for TOPOLGY

Originally Posted by kaptain483
how do you show that they are pair wise disjoint sets
To do topology one must know the definitions.

Post the definitions of interior point, boundary point, and exterior point.

Then use those definitions to show that none of those overlap.

This is your problem to do, so show some effort.