Definition:Separated by Neighborhoods/Points

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Definition 2
Thus two points $x$ and $y$ are separated by neighborhoods the two singleton sets $\left\{{x}\right\}$ and $\left\{{y}\right\}$ are separated by neighborhoods as sets.

Also see

 * Equivalence of Definitions of Points Separated by Neighborhoods

Generalizations

 * Definition:Sets Separated by Neighborhoods

Weaker conditions

 * Definition:Separated Points

Stronger conditions

 * Definition:Points Separated by Closed Neighborhoods