Question about interior.

  • Thread starter cragar
  • Start date
  • #1
2,544
2

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
22,097
3,280
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.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
955
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.
 

Related Threads on Question about interior.

  • Last Post
Replies
10
Views
4K
Replies
3
Views
535
Replies
3
Views
1K
Replies
3
Views
4K
Replies
5
Views
754
Top