# 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 Isolated 2013-03-22 12:05:59 2013-03-22 12:05:59 djao (24) djao (24) 8 djao (24) Definition msc 54A05 discrete set isolated set isolated point