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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Co-elementary equivalence, co-elementary maps, and generalized arcs
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by Paul Bankston PDF
Proc. Amer. Math. Soc. 125 (1997), 3715-3720 Request permission


By a generalized arc we mean a continuum with exactly two non-separating points; an arc is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any two generalized arcs are co-elementarily equivalent, and that co-elementary images of generalized arcs are generalized arcs. We also show that if $f:X \to Y$ is a function between compacta and if $X$ is an arc, then $f$ is a co-elementary map if and only if $Y$ is an arc and $f$ is a monotone continuous surjection.
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Additional Information
  • Paul Bankston
  • Affiliation: Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53201-1881
  • Email:
  • Received by editor(s): July 2, 1996
  • Communicated by: Andreas R. Blass
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3715-3720
  • MSC (1991): Primary 03C20, 54B35, 54C10, 54D05, 54D30, 54D80, 54F05, 54F15
  • DOI:
  • MathSciNet review: 1422845