Let $(X, \mathfrak T)$ be a topological space and supposed that $A$ is a subset of $X$ then the Bd(A) is a closed set.
I am in an introduction to proofs class. I have to decided if this is a true or false statement. If true, prove and if false, give a counterexample.
My definition of boundary is " Let $(X,\mathfrak T)$ be a topological space and let $A \subseteq X$. A point $x \in X$ is in the boundary of $A$ if every open set containing $x$ intersects both $A$ and $X−A$.
I think this is a true statement and I would like to show that by showing that the complement of an open set is closed. Showing that the points not in a boundary of a set are an open set. Is this the right track to take?