Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $1/k$-homogeneous long solenoids   We study nonmetric analogues of Vietoris solenoids. Let $\Lambda$ be an
ordered continuum, and let $\vec{p}=\langle p_1,p_2,\dots\rangle$ be a sequence
of positive integers. We define a natural inverse limit space
$S(\Lambda,\vec{p})$, where the first factor space is the nonmetric "circle"
obtained by identifying the endpoints of $\Lambda$, and the $n$th factor space,
$n>1$, consists of $p_1p_2\cdot\dots \cdot p_{n-1}$ copies of $\Lambda$ laid
end to end in a circle. We prove that for every cardinal $\kappa\geq 1$, there
is an ordered continuum $\Lambda$ such that $S(\Lambda,\vec{p})$ is
$\frac{1}{\kappa}$-homogeneous; for $\kappa>1$, $\Lambda$ is built from copies
of the long line. Our example with $\kappa=2$ provides a nonmetric answer to a
question of Neumann-Lara, Pellicer-Covarrubias and Puga-Espinosa from 2005, and
with $\kappa=1$ provides an example of a nonmetric homogeneous circle-like
indecomposable continuum. Finally, we employ a cohomology argument to prove
that for each ordered continuum $\Lambda$, as $\vec{p}$ varies there are
$2^\omega$-many nonhomeomorphic spaces $S(\Lambda,\vec{p})$.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph