Definition:Open Set (Neighborhood Space)

Definition

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

Let $U \subseteq S$ be a neighborhood of each of its elements.

Then $U$ is an open set of $S$.

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $3$: Topological Spaces: $\S 3$: Neighborhoods and Neighborhood Spaces: Definition $3.5$