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

What is it about?

Usually manifolds are assumed to be second countable by definition. While this assumption always holds for the important examples of manifolds arrising in physics, one looses many interesting examples with this assumption. In this publication it is proven that manifolds (even without being second countable) can be embedded as submanifolds if one allows the surrounding space to be infinite dimensional.

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Why is it important?

Differential topology of manifolds which are not second countable is still at its very beginning. This article can be seen as one step in better understanding these interesting strange objects, connecting them with the world of infinite dimensional differential calculus.