Does Cl(X-A)=X-Int(A) work in infinite and uncountable dimensions?

[cragar]

If I have the statement Cl(X-A)=X-Int(A)
X and A are topological spaces. Does this statement work in infinite dimensions and uncountable dimensions. I think it would just wondering.

 

[micromass]

If I have the statement Cl(X-A)=X-Int(A)
X and A are topological spaces. Does this statement work in infinite dimensions and uncountable dimensions. I think it would just wondering.

What do you mean with "dimension" in topology in the first place?

But yes, the statement is always true as you can easily check for yourself.

 

[HallsofIvy]

Most topological spaces do define "dimension". Nor does it make sense to talk about X and A both being topologica spaces. I think you mean X is a topological space and A is a subset of X. But it is true that in any topological space that the closure of X- A is X- the interior of A.