Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the dichotomy of a locally compact semitopological monoid of order
  isomorphisms between principal filters of $\mathbb{N}^n$ with adjoined zero   Let $n$ be any positive integer and $\mathscr{I\!P\!F}(\mathbb{N}^n)$ be the
semigroup of all order isomorphisms between principal filters of the $n$-th
power of the set of positive integers $\mathbb{N}$ with the product order. We
prove that a Hausdorff locally compact semitopological semigroup
${\mathscr{I\!P\!F}(\mathbb{N}^n)}$ with an adjoined zero is either compact or
discrete.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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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: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol