Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Countable dense homogeneity and the Cantor set   It is shown that CH implies the existence of a compact Hausdorff space that
is countable dense homogeneous, crowded and does not contain topological copies
of the Cantor set. This contrasts with a previous result by the author which
says that for any crowded Hausdorff space $X$ of countable $\pi$-weight, if
${}^\omega{X}$ is countable dense homogeneous, then $X$ must contain a
topological copy of the Cantor set.

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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int