1st December 2004

Munkres §36

Ex. 36.1. Any locally euclidean space is locally compact (as open subspaces of euclidean space are locally compact [Cor 29.3]). A manifold is locally euclidean and Hausdorff, so it is locally compact Hausdorff, hence regular [Ex 32.3]. A manifold also has a countable basis, so it is normal [Thm 32.1] and metrizable [Thm 34.1].

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