Definition:Topological Space Induced by Neighborhood Space

Definition
Let $\left({S, \mathcal N}\right)$ be a neighborhood space.

Let $\tau$ be the set of open sets of $\left({S, \mathcal N}\right)$.

Then $\left({S, \tau}\right)$ is the topological space induced by $\left({S, \mathcal N}\right)$.

Also known as
Some sources refer to $\left({S, \tau}\right)$ in this context as the topological space given rise to by $\left({S, \mathcal N}\right)$.

Also see

 * Topological Space Induced by Neighborhood Space is Topological Space