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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
There are 30 references to this entry.

This is version 4 of isolated, born on 2002-01-04, modified 2006-10-03.
Object id is 1201, canonical name is Isolated.
Accessed 6832 times total.

Classification:
AMS MSC: 54A05 (General topology :: Generalities :: Topological spaces and generalizations )
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