Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oscillation of Urysohn type spaces   A metric space $\mathrm{M}=(M;\de)$ is {\em homogeneous} if for every
isometry $\alpha$ of a finite subspace of $\mathrm{M}$ to a subspace of
$\mathrm{M}$ there exists an isometry of $\mathrm{M}$ onto $\mathrm{M}$
extending $\alpha$. The metric space $\mathrm{M}$ is {\em universal} if it
isometrically embeds every finite metric space $\mathrm{F}$ with
$\dist(\mathrm{F})\subseteq \dist(\mathrm{M})$. ($\dist(\mathrm{M})$ being the
set of distances between points of $\mathrm{M}$.)
  A metric space $\mathrm{M}$ is {\em oscillation stable} if for every
$\epsilon>0$ and every uniformly continuous and bounded function $f: M\to \Re$
there exists an isometric copy $\mathrm{M}^\ast=(M^\ast; \de)$ of $\mathrm{M}$
in $\mathrm{M}$ for which: \[ \sup\{|f(x)-f(y)| \mid x,y\in M^\ast\}<\epsilon.
\]
  Every bounded, uncountable, separable, complete, homogeneous, universal
metric space $\mathrm{M}=(M;\de)$ is oscillation stable. (Theorem
thm:finabstr.)

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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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: cs
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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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: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga