Prove or Disprove: Closure of Int(X)=X

[julia89]

Prove or disprove

Closure of the Interior of a closed set X is equal to X
so clos(intX)=X

I think it is true, but i don't know how to prove it

I thought that clos(int(X))=int(X)+bdy(int(X))=X


thanks,

julia

 

[HallsofIvy]

Think carefully. Consider the singleton set {p} containing only the single point p. In any metric topology, such a set is closed. What is its interior? What is the closure of that interior.

 

[Pere Callahan]

What if the interior is non-empty?