Definition:Topological Space Induced by Neighborhood Space

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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


Sources