Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closure operations, Continuous valuations on monoids and Spectral spaces   We present several naturally occurring classes of spectral spaces using
commutative algebra on pointed monoids. For this purpose, our main tools are
finite type closure operations and continuous valuations on monoids which we
introduce in this work. In the process, we make a detailed study of different
closure operations on monoids. We prove that the collection of continuous
valuations on a topological monoid with topology determined by any finitely
generated ideal is a spectral space.

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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys