I am have run into a problem where I am supposed to prove that for any set A, the boundary of A is a closed set and that for any set A, the boundary of A is a subset of A closure.
I am have run into a problem where I am supposed to prove that for any set A, the boundary of A is a closed set and that for any set A, the boundary of A is a subset of A closure.
Let $\displaystyle A^o,~\beta(A),~\&~\mathcal{E}(A)$ stand for interior, boundary, and exterior of the set $\displaystyle A$.
Now you use basic definitions show those are pair-wise disjoint sets.
If you can do that, then this question is obviously true.