Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Each regular paratopological group is completely regular   We prove that a semiregular topological space $X$ is completely regular if
and only if its topology is generated by a normal quasi-uniformity. This
characterization implies that each regular paratopological group is completely
regular. This resolves an old problem in the theory of paratopological groups,
which stood open for about 60 years. Also we define a natural uniformity on
each paratopological group and using this uniformity prove that each (first
countable) Hausdorff paratopological group is functionally Hausdorff (and
submetrizable). This resolves another two known open problems in the theory of
paratopological groups.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio