isolated

Let $X$ be a topological space, let $S\subset X$, and let $x\in S$. The point $x$ is said to be an isolated point of $S$ if there exists an open set $U\subset X$ such that $U\cap S=\{x\}$.

The set $S$ is isolated or discrete if every point in $S$ is an isolated point.

Title	isolated
Canonical name	Isolated
Date of creation	2013-03-22 12:05:59
Last modified on	2013-03-22 12:05:59
Owner	djao (24)
Last modified by	djao (24)
Numerical id	8
Author	djao (24)
Entry type	Definition
Classification	msc 54A05
Synonym	discrete set
Defines	isolated set
Defines	isolated point