Equivalent metrics and the spans of graphs

Volume 114 / 2009

L. C. Hoehn, A. Karassev Colloquium Mathematicum 114 (2009), 135-153 MSC: 54E35, 54F15, 54F50. DOI: 10.4064/cm114-1-11


We present a result which affords the existence of equivalent metrics on a space having distances between certain pairs of points predetermined, with some restrictions. This result is then applied to obtain metric spaces which have interesting properties pertaining to the span, semispan, and symmetric span of metric continua. In particular, we show that no two of these variants of span agree for all simple closed curves or for all simple triods.


  • L. C. HoehnDepartment of Mathematics
    University of Toronto
    40 St. George Street
    Toronto, ON, Canada M5S 2E4
  • A. KarassevComputer Science and Mathematics Department
    Nipissing University
    100 College Drive, Box 5002
    North Bay, ON, Canada P1B 8L7

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