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
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $3$: Topological Spaces: $\S 3$: Neighborhoods and Neighborhood Spaces