# Thread: Set Question, deleted neighborhood

1. ## Set Question, deleted neighborhood

For this question,

Prove: for each x in R and $\varepsilon > 0$, $N^*(x , \varepsilon)$ is an open set.

why does it suffice to show that the set is open by showing that every point of the set is an interior point?

EDIT: sorry if this or any of some of my future questions are trivial, i think this one is, but my professor has been hard to reach these past 2 weeks.

2. Originally Posted by p00ndawg
For this question,

Prove: for each x in R and $\varepsilon > 0$, $N^*(x , \varepsilon)$ is an open set.

why does it suffice to show that the set is open by showing that every point of the set is an interior point?

EDIT: sorry if this or any of some of my future questions are trivial, i think this one is, but my professor has been hard to reach these past 2 weeks.
An open set is defined to be a set such that all it's points are interior points.