Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Examples and counterexamples of type I isometric shifts   We provide examples of nonseparable spaces $X$ for which C(X) admits an
isometric shift of type I, which solves in the negative a problem proposed by
Gutek {\em et al.} (J. Funct. Anal. {\bf 101} (1991), 97-119). We also give two
independent methods for obtaining separable examples. The first one allows us
in particular to construct examples with infinitely many nonhomeomorphic
components in a subset of the Hilbert space $\ell^2$. The second one applies
for instance to sequences adjoined to any n-dimensional compact manifold (for
$n \ge 2$) or to the Sierpi\'nski curve. The combination of both techniques
lead to different examples involving a convergent sequence adjoined to the
Cantor set: one method for the case when the sequence converges to a point in
the Cantor set, and the other one for the case when it converges outside.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga