---
type: "concept"
title: "Topological manifold"
slug: "topological-manifold"
language: "en"
translationGroupId: "cmrnenyng0013ki01pr631f0n"
domain: "General topology"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

A topological manifold of dimension $n$ is a [[Topological space|topological space]] $M$ that is [[Hausdorff space|Hausdorff]], [[Second-countable space|second-countable]], and that is locally euclidean, that is, every point of $M$ has an [[Open neighborhood|open neighborhood]] that is [[Homeomorphism|homeomorphic]] to an [[Open set|open subset]] of $\R^{n}$.