# Homework Help: Interior of a set

1. Sep 13, 2012

### cragar

1. The problem statement, all variables and given/known data
Consider the excluded point topology on a set X.
Determine Int(A) and Cl(A) for sets A containing p and for sets A not containing p.
Excluded point topology is all the subsets of X that exclude p.
where p is in X.
3. The attempt at a solution
So the interior of a set A is the union of all open sets contained in A.
Would the interior for A be A-p , where we exclude p.
and would the interior be A where we include p.
Im not sure what the smallest closed set would be that contains A.
It seem like it would just be A.

2. Sep 13, 2012

### SammyS

Staff Emeritus

If p∈A,
Determine Int(A).

Determine Cl(A).​

If p∉A,
Determine Int(A).

Determine Cl(A).​

3. Sep 14, 2012

### cragar

for the closure of those sets, should I try a proof by contradiction.
for the second one assume that p is not in the closure.Since p is not in A it is in the complement so it is in a closed set.

4. Sep 14, 2012

### clamtrox

Have you proven any properties for closure and interior? For example, you can show that interior of A is the largest open set contained in A and closure of A is the smallest closed set which contains A. If you can prove this, then you're almost done.

5. Sep 14, 2012

### SammyS

Staff Emeritus
If $p\in\text{A}\,,$ then is set A open or is A closed?
If $p\notin\text{A}\,,$ then is set A open or is A closed?