Definition:Topological Space Induced by Neighborhood Space

Definition
Let $\struct {S, \NN}$ be a neighborhood space.

Let $\tau$ be the set of open sets of $\struct {S, \NN}$.

Then $\struct {S, \tau}$ is the topological space induced by $\struct {S, \NN}$.

Also known as
Some sources refer to $\struct {S, \tau}$ in this context as the topological space given rise to by $\struct {S, \NN}$.

Also see

 * Topological Space Induced by Neighborhood Space is Topological Space