Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformity of uniform convergence on the family of sets   We prove that for every Hausdorff space X and any uniform quadra space (Y,U)
the topology on C(X,Y) induced by the uniformity U| of uniform convergence on
the saturation family L coincides with the set-open topology on C(X,Y). In
particular, for every pseudocompact space X and any metrizable topological
vector space Y with uniform U the topology on C(X,Y) induced by the uniformity
U| of uniform convergence coincides with the C-compact-open topology on C(X,Y),
and depends only on the topology induced on Y by the uniformity U. It is also
shown that in the class closed-homogeneous complete uniform spaces Y necessary
condition for coincidence of topologies is Y-compactness of elements of family
L.

12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: stat