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Continuous curves of nonmetric pseudo-arcs and semi-conjugacies to interval maps

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Jan P. Boronski, Michel Smith

General Topology · Submitted 7 Jan 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Extending his approach, and the results of Lewis on lifting homeomorphisms, we construct a nonmetric pseudo-circle, and new examples of homogeneous 1-dimensional continua; e.g. a circle and solenoids of nonmetric pseudo-arcs.

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arXiv ID1701.01862 (version 2)
Pith IDWT56KRQ3, Pith's permanent record of this paper and its review
CitationJan P. Boronski, Michel Smith. "Continuous curves of nonmetric pseudo-arcs and semi-conjugacies to interval maps." arXiv:1701.01862 (2017). https://pith.science/paper/WT56KRQ3
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,892 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.86 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In 1985 M. Smith constructed a nonmetric pseudo-arc; i.e. a Hausdorff homogeneous, hereditary equivalent and hereditary indecomposable continuum. Taking advantage of a decomposition theorem of W. Lewis, he obtained it as a long inverse limit of metric pseudo-arcs with monotone bonding maps. Extending his approach, and the results of Lewis on lifting homeomorphisms, we construct a nonmetric pseudo-circle, and new examples of homogeneous 1-dimensional continua; e.g. a circle and solenoids of nonmetric pseudo-arcs. Among many corollaries we also obtain an analogue of another theorem of Lewis from 1984: any interval map is semi-conjugate to a homeomorphism of the nonmetric pseudo-arc.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In 1985 M. background 0.99 0.04 0.01 unclear 0.98
s1 Smith constructed a nonmetric pseudo-arc; i.e. a Hausdorff homogeneous, hereditary equivalent and hereditary indecomposable continuum. background 1.00 0.04 0.06 asserted 1.00
s2 Taking advantage of a decomposition theorem of W. method 0.83 0.24 0.02 unclear 0.56
s3 Lewis, he obtained it as a long inverse limit of metric pseudo-arcs with monotone bonding maps. method 0.52 0.30 0.05 asserted 1.00
s4 Extending his approach, and the results of Lewis on lifting homeomorphisms, we construct a nonmetric pseudo-circle, and new examples of homogeneous 1-dimensional continua; e.g. a circle and solenoids of nonmetric pseudo-arcs. contribution 0.95 0.95 0.47 asserted 1.00
s5 Among many corollaries we also obtain an analogue of another theorem of Lewis from 1984: any interval map is semi-conjugate to a homeomorphism of the nonmetric pseudo-arc. result 0.97 0.78 0.44 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In 1985 M. Smith constructed a nonmetric pseudo-arc; i.e. a Hausdorff homogeneous, hereditary equivalent and hereditary indecomposable continuum. Taking advantage of a decomposition theorem of W. Lewis, he obtained it as a long inverse limit of metric pseudo-arcs with monotone bonding maps. Extending his approach, and the results of Lewis on lifting homeomorphisms, we construct a nonmetric pseudo-circle, and new examples of homogeneous 1-dimensional continua; e.g. a circle and solenoids of nonmetric pseudo-arcs. Among many corollaries we also obtain an analogue of another theorem of Lewis from 1984: any interval map is semi-conjugate to a homeomorphism of the nonmetric pseudo-arc.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as support 1 paper
  • Moreover Smith's nonmetric pseudo-arc has recently provided another counterexample to Wood's conjecture [ref] , which highlights the importance of including the nonmetric hereditarily indecomposable continua in future studies.

    On the conjecture of Wood and projective homogeneity · Introduction · 0.96

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