Boundary and closure relationship

[gamitor]

Dear all,

How can I show that:

The boundary of a set S is equal to the intersection of the closure and the closure of the complement of S ?

Thanks a lot in advance

 

[CompuChip]

Can you give us the definition of "closure" and "boundary"?

(That's not just because I want to force you to use the Homework questions template, but in different domains of mathematics there are different definitions of those concepts, so it's important to know which ones you are using).

 

[gamitor]

Can you give us the definition of "closure" and "boundary"?

(That's not just because I want to force you to use the Homework questions template, but in different domains of mathematics there are different definitions of those concepts, so it's important to know which ones you are using).

The definitions are in the following images. I tried to do it by the definitions or by the Boundary=Closure\Interior but I couldn't.

Any help would be highly appreciated