Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arhangel'ski\u{\i} sheaf amalgamations in topological groups   We consider amalgamation properties of convergent sequences in topological
groups and topological vector spaces. The main result of this paper is that,
for arbitrary topological groups, Nyikos's property $\alpha_{1.5}$ is
equivalent to Arhangel'ski\u{\i}'s formally stronger property $\alpha_1$. This
result solves a problem of Shakhmatov (2002), and its proof uses a new
perturbation argument. We also prove that there is a topological space $X$ such
that the space $C_p(X)$ of continuous real-valued functions on $X$, with the
topology of pointwise convergence, has Arhangel'ski\u{\i}'s property $\alpha_1$
but is not countably tight. This result follows from results of
Arhangel'ski\u{\i}--Pytkeev, Moore and Todor\v{c}evi\'c, and provides a new
solution, with remarkable properties, to a problem of Averbukh and Smolyanov
(1968) concerning topological vector spaces. The Averbukh--Smolyanov problem
was first solved by Plichko (2009), using Banach spaces with weaker locally
convex topologies.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: stat