Last Updated：2025/11/24

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(topology) Given a subset S of a given topological space T, any point p whose every neighborhood contains some point, distinct from p, which belongs to S.

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limit point

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Source Word

limit point

Noun

Japanese Meaning

位相空間において、ある集合Sの極限点とは、どの近傍も必ずその点自身とは異なる、Sに属する点を含むような点のことを指す。

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In the standard topology on R, 0 is a limit point of the set {1/n : n ∈ N} because every neighborhood of 0 contains some 1/n distinct from 0.

Google Translation / DeepL Translation

標準位相を持つ実数直線では、0は集合{1/n : n∈N}の極限点であり、0の任意の近傍には0と異なる1/nが含まれる。

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Sense（1）

sin ( cot 1/z)

is an example of a function having infinitely many essential singularities with a limit point at z=0. It is an easy matter to give examples of "elementary" functions whose singularities have a countable number of limit points.

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limit points

（ plural ）

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limit point

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limit point

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