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isolated (Definition)

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.




"isolated" is owned by djao.
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Other names:  discrete set
Also defines:  isolated set, isolated point
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Cross-references: discrete, open set, point, topological space
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This is version 4 of isolated, born on 2002-01-04, modified 2006-10-03.
Object id is 1201, canonical name is Isolated.
Accessed 9170 times total.

Classification:
AMS MSC54A05 (General topology :: Generalities :: Topological spaces and generalizations )

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