Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A combinatorial model for the Menger curve   We represent the universal Menger curve as the topological realization
$|\mathbb{M}|$ of the projective Fra\"iss\'e limit ${\mathbb M}$ of the class
of all finite connected graphs. We show that $\mathbb{M}$ satisfies
combinatorial analogues of the Mayer-Oversteegen-Tymchatyn homogeneity theorem
and the Anderson-Wilson projective universality theorem. Our arguments involve
only $0$-dimensional topology and constructions on finite graphs. Using the
topological realization $\mathbb{M}\mapsto|\mathbb{M}|$, we transfer some of
these properties to the Menger curve: we prove the approximate projective
homogeneity theorem, recover Anderson's finite homogeneity theorem, and prove a
variant of Anderson-Wilson's theorem. The finite homogeneity theorem is the
first instance of an "injective" homogeneity theorem being proved using the
projective Fra\"iss\'e method. We indicate how our approach to the Menger curve
may extend to higher dimensions.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: q-fin