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# 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.

Defines:

isolated set, isolated point

Synonym:

discrete set

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

54A05*no label found*

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## Comments

## equivalent definition

A point x in S is an isolated point if and only if {x} is open in S.