Interior and Closure for TOPOLGY

• Feb 8th 2013, 02:44 PM
kaptain483
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.
• Feb 8th 2013, 02:56 PM
Plato
Re: Interior and Closure for TOPOLGY
Quote:

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.
• Feb 10th 2013, 06:52 PM
kaptain483
Re: Interior and Closure for TOPOLGY
how do you show that they are pair wise disjoint sets
• Feb 10th 2013, 07:14 PM
Plato
Re: Interior and Closure for TOPOLGY
Quote:

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.