Isolated 2002-01-04 01:47:55 2006-10-03 14:39:18 Definition isolated set isolated point \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $X$ be a topological space, let $S \subset X$, and let $x \in S$. The point $x$ is said to be an \emph{isolated} point of $S$ if there exists an open set $U \subset X$ such that $U \cap S = \{x\}$. The set $S$ is \emph{isolated} or \emph{discrete} if every point in $S$ is an isolated point.