Definition:Separated Points

Definition

Let $\struct {S, \tau}$ 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

• Definition:Separated Sets

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): separated points