# Set Question, deleted neighborhood

• Dec 16th 2009, 10:19 AM
p00ndawg
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.
• Dec 16th 2009, 09:44 PM
Drexel28
Quote:

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.