Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology on locally finite metric spaces   The necessity of a theory of General Topology and, most of all, of Algebraic
Topology on locally finite metric spaces comes from many areas of research in
both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry,
Computer Science, Topological Graph Theory and Metric Geometry. In this paper
we propose the basic notions of such a theory and some applications: we replace
the classical notions of continuous function, homeomorphism and homotopic
equivalence with the notions of NPP-function, NPP-local-isomorphism and
NPP-homotopy (NPP stands for Nearest Point Preserving); we also introduce the
notion of NPP-isomorphism. We construct three invariants under NPP-isomorphisms
and, in particular, we define the fundamental group of a locally finite metric
space. As first applications, we propose the following: motivated by the
longstanding question whether there is a purely metric condition which extends
the notion of amenability of a group to any metric space, we propose the
property SN (Small Neighborhood); motivated by some applicative problems in
Computer Science, we prove the analog of the Jordan curve theorem in $\mathbb
Z^2$; motivated by a question asked during a lecture at Lausanne, we extend to
any locally finite metric space a recent inequality of P.N.Jolissaint and
Valette regarding the $\ell_p$-distortion.

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an