Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformly joinable, locally uniformly joinable, and weakly chained
  uniform spaces   Brodskiy, Dydak, LaBuz, and Mitra introduced the concepts of uniform
joinability and local uniform joinability for uniform spaces when developing
their theory of generalized uniform covering maps which was motivated by a
paper by Berestovskii and Plaut. (Local) uniform joinability can be thought of
as analogous to (local) path connectedness. A chain connected locally uniformly
joinable uniform space is uniformly joinable. This note gives an example of a
metric space that is uniformly joinable but not locally uniformly joinable.
  Plaut recently defined the concept of a weakly chained uniform space. We show
that a weakly chained metrizable uniform space is locally uniformly joinable.
Since local uniform joinability is equivalent to pointed 1-movability for
metric continua, we find that weak chainability is equivalent to pointed
1-movability for such spaces.

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The categories of this paper are: cs
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex