Definition:Separated Points

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Definition

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

Let $x, y \in S$ such that both of the following hold:

  • $\exists U \in \tau: x \in U, y \notin U$
  • $\exists V \in \tau: y \in V, x \notin V$


Then $x$ and $y$ are separated points.


Also see

Generalizations