Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces

Rafael Dahmen

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arXiv · 1503.05770

Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces

Rafael Dahmen

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Abstract

We show that every finite dimensional Hausdorff (not necessarily paracompact, not necessarily second countable) $C^r$-manifold can be embedded into a weakly complete vector space, i.e. a locally convex topological vector space of the form ${\mathbb R}^I$ for an uncountable index set $I$ and determine the minimal cardinality of $I$ for which such an embedding is possible.

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BibTeX RIS

Rafael Dahmen. 2015-03-26. Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces. https://arxiv.org/abs/1503.05770

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