Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polish topologies on groups of non-singular transformations   In this paper, we prove several results concerning Polish group topologies on
groups of non-singular transformation. We first prove that the group of
measure-preserving transformations of the real line whose support has finite
measure carries no Polish group topology. We then characterize the Borel
$\sigma$-finite measures $\lambda$ on a standard Borel space for which the
group of $\lambda$-preserving transformations has the automatic continuity
property. We finally show that the natural Polish topology on the group of all
non-singular transformations is actually its only Polish group topology.

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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci