# Interior, exterior and boundary of a set in the discrete topology

For a set X with the discrete topology, show that for every $A\subset X$:

1. $\text{int} A = A$
2. $\text{ext} A = X\setminus A$
3. $\partial A = \emptyset$

where int means the interior of $A$, ext means the exterior of $A$, and $\partial A$ is the boundary of $A$.

Well, I try by the open sets but I got nowhere... Then I try by neighborhood and I got nowhere...

Of course that the proof of the boundary of A is really obvious, but I can't do the int....can somebody help?

• Maybe you could add to your question what you consider the definition of $\operatorname{int} A$. (This might help user answering your question to provide an answer which suits your needs.) – Martin Sleziak Dec 11 '15 at 4:09