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Lifting paths on quotient spaces

机译：商空间上的提升路径

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摘要

Let X be a compactum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an ordered compactum. If the quotient space X/G is the continuous image of an ordered compactum, under what conditions is X also the continuous image of an ordered compactum? Examples around the (non-metric) Hahn-Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. We prove that the compactum X is the image of an ordered compactum when each g ∈ G has 0-dimensional boundary. We also consider the case when G has only countably many non-degenerate elements. These results extend earlier work of the first named author in a number of ways.
机译：令X为紧致粉，G为X的上半连续分解，使得G的每个元素为有序紧致粉的连续图像。如果商空间X / G是有序紧致的连续图像，那么X在什么条件下也是有序紧致的连续图像？关于（非度量）Hahn-Mazurkiewicz定理的例子表明，如果一个人希望获得积极的结果，就必须对G施加严格的条件。我们证明，当每个g∈G具有0维边界时，紧致粉X是有序紧致粉的图像。我们还考虑了G仅具有许多非退化元素的情况。这些结果以多种方式扩展了第一位具名作者的早期工作。

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  • 来源
    《Topology and its applications》 |2009年第9期|1739-1745|共7页
  • 作者

    D. Daniel; J. Nikiel; L.B. Treybig; M. Tuncali; E.D. Tymchatyn;

  • 作者单位

    Lamar University, Department of Mathematics, Beaumont, TX 77710, USA;

    Opole University, Institute of Mathematics and Informatics, ul. Oleska 48,45-052 Opole, Poland;

    Texas A&M University, Department of Mathematics. College Station, TX 77843, USA;

    Nipissing University, Faculty of Arts and Sciences, North Bay, Ontario P1B 8L7, Canada;

    University of Saskatchewan, Department of Mathematics, Saskatoon, Saskatchewan S7N 0W0, Canada;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    ordered continuum; null family; decomposition; lifting images of arcs;

    机译：有序连续体空家庭分解;弧形提升图像;

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