Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Big Free Groups are Almost Free   It is shown that the big free group (the set of countably-long words over a
countable alphabet) is almost free, in the sense that any function from the
alphabet to a compact topological group factors through a homomorphism. This
statement is in fact a simple corollary of the more general result proven below
on the extendability of homomorphisms from subgroups (of a certain kind) of the
big free group to a compact topological group.

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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph