# Math Help - Interior point

1. ## Interior point

Help me please. I can not prove the following.

Prove that a point belongs to the lock of $A$ if and only if is a interior point or a frontier point of $A$.

Thanks

2. Originally Posted by osodud
Prove that a point belongs to the lock of $A$ if and only if is a interior point or a frontier point of $A$.
Some translations are in order here.
‘lock’ must mean closure; ‘frontier’ must mean boundary.

A point is in the closure of the set iff every open set containing the point contains a point of the set.

Thus, if we have a interior point or a frontier point of $A$ then by definition it is in the closure.

Suppose $p\in \overline{A}$, the closure.
If $p$ is an interior point of $A$ we are done.
So what does it mean to say that $p$ is not an interior point?
Now you need to consider two cases: $p\in A~\&~p\notin A$.
Both cases should force $p$ to be a boundary point.