(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that every topological manifold is homeomorphic to some subspace of E^n, i.e., n-dimensional Euclidean space.

2. Relevant equations

A topological manifold is a Hausdorff space that are locally Euclidean, i.e., there's an n such that for each x, there's a neighborhood N(x) homeomorphic to E^n.

3. The attempt at a solution

This must be well known, but I have no idea how to start. How would I construct the E^n subspace and the corresponding homeomorphic mapping? By definition, there's a different mapping for each point. Thank you for your help.

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# Homework Help: Prove that topological manifold homeomorphic to Euclidean subspace

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