Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth embeddings of the Long Line and other non-paracompact manifolds
  into locally convex spaces   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.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg