Geodesic
Equivalent metrics and the spans of graphs
L. C. Hoehn 1   ; A. Karassev 2
1 Department of Mathematics University of Toronto 40 St. George Street Toronto, ON, Canada M5S 2E4
2 Computer Science and Mathematics Department Nipissing University 100 College Drive, Box 5002 North Bay, ON, Canada P1B 8L7
Colloquium Mathematicum, Tome 114 (2009) no. 1, pp. 135-153 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm114-1-11
Keywords: present result which affords existence equivalent metrics space having distances between certain pairs points predetermined restrictions result applied obtain metric spaces which have interesting properties pertaining span semispan symmetric span metric continua particular these variants span agree simple closed curves simple triods

L. C. Hoehn  1   ; A. Karassev  2

1 Department of Mathematics University of Toronto 40 St. George Street Toronto, ON, Canada M5S 2E4
2 Computer Science and Mathematics Department Nipissing University 100 College Drive, Box 5002 North Bay, ON, Canada P1B 8L7 
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L. C. Hoehn; A. Karassev. Equivalent metrics and the spans of graphs. Colloquium Mathematicum, Tome 114 (2009) no. 1, pp. 135-153. doi: 10.4064/cm114-1-11

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