Definition:System of Open Neighborhoods

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $x \in S$.

Let $\map \UU x$ be the set of all open neighborhoods of $x$ in $T$.

Then $\map \UU x$ is the system of open neighborhoods of the point $x$.

Also see

• Results about systems of open neighborhoods can be found here.

Sources

• 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter $1$: Spaces and Lattices of Open Sets, $\S 1$ Sober spaces, Definition $1.3$