Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Measure-Expansive Diffeomorphisms   In this note we prove that a homeomorphism is countably-expansive if and only
if it is measure-expansive. This result is applied for showing that the
$C^1$-interior of the sets of expansive, measure-expansive and continuum-wise
expansive $C^1$-diffeomorphisms coincide.

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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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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: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: nlin
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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: cond-mat
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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