Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological groups with invariant linear spans   Given a topological group $G$ that can be embedded as a topological subgroup
into some topological vector space (over the field of reals) we say that $G$
has invariant linear span if all linear spans of $G$ under arbitrary embeddings
into topological vector spaces are isomorphic as topological vector spaces.
  For an arbitrary set $A$ let $\mathbb{Z}^{(A)}$ be the direct sum of
$|A|$-many copies of the discrete group of integers endowed with the Tychonoff
product topology. We show that the topological group $\mathbb{Z}^{(A)}$ has
invariant linear span. This answers a question of D. Dikranjan et al. in
positive.
  We prove that given a non-discrete sequential space $X$, the free abelian
topological group $A(X)$ over $X$ is an example of a topological group that
embeds into a topological vector space but does not have invariant linear span.

11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org