Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar embeddings of chainable continua   We prove that for a chainable continuum $X$ and every non-zigzag $x\in X$
there exists a planar embedding $\phi:X\to \phi(X)\subset\mathbb R^2$ such that
$\phi(x)$ is accessible, partially answering the question of Nadler and Quinn
from 1972. Two embeddings $\phi,\psi:X \to \mathbb R^2$ are called strongly
equivalent if $\phi \circ \psi^{-1}: \psi(X) \to \phi(X)$ can be extended to a
homeomorphism of $\mathbb R^2$. We also prove that every indecomposable
chainable continuum can be embedded in the plane in uncountably many strongly
non-equivalent ways.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an