# Isolated point

In a

topological space *X*, an

**isolated point** is a point

*x* such that the singleton {

*x*} is

open. Equivalently,

*x* is an isolated point if

*x* is not a

limit point of

*X*. If

*A* is a subset of

*X*, we say that

*x* is an isolated point of

*A* if

*x* is an isolated point of the

subspace *A*.

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