---
tag: 0E3X7TXS67
kind: concept
name: Limit point
aliases: [accumulation-point, cluster-point]
msc: [54A05]
sources:
  - url: https://en.wikipedia.org/wiki/Accumulation_point
    locator: lead section
same_as:
  wikidata: Q858223
  wikipedia: Accumulation point
---

## Summary

A limit point of a set $S$ is a point $x$ such that each neighbourhood of $x$ contains a point of $S$ other than $x$.
Limit points are the points that the subset approaches without using the point itself.