Isolated Point

(General Topology)

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General Topology
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What is Isolated point?

In mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S but there exists a neighborhood of x which does not contain any other points of S. This is equivalent to saying that the singleton {x} is an open set in the topological space S (considered as a subspace of X). If the space X is a Euclidean space (or any other metric space), then x is an isolated point of S if there exists an open ball around x which contains no other points of S. (Introducing the notion of sequences and limits, one can say equivalently that an element x of S is an isolated point of S if and only if it is not a limit point of S.)

Technology Types

general topology

Synonyms

Discrete setDiscrete subsetHermit Point

Translations

Geïsoleerd punt (nl)Isolierter Punkt (de)Izolita punkto (eo)Point isolé (fr)Ponto isolado (pt)Punto aislado (es)Punto isolato (it)Titik pencil (in)Zbiór dyskretny (pl)Изолированная точка множества (ru)Ізольована точка (uk)نقطة معزولة (ar)고립점 (ko)孤点 (zh)孤立点 (ja)

Tech Info


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 — Date merged: 11/6/2021, 1:32:52 PM
 — Date scraped: 5/20/2021, 6:15:22 PM