Real Open Sets
Definition
A subset $U \subset \R ^n$ is open if for every point $x \in U$ there exists a real number $\epsilon > 0$ so that $B(x, \epsilon ) \subset U$.
A subset $U \subset \R ^n$ is open if for every point $x \in U$ there exists a real number $\epsilon > 0$ so that $B(x, \epsilon ) \subset U$.