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Co-elementary equivalence, co-elementary maps, and generalized arcs


Author: Paul Bankston
Journal: Proc. Amer. Math. Soc. 125 (1997), 3715-3720
MSC (1991): Primary 03C20, 54B35, 54C10, 54D05, 54D30, 54D80, 54F05, 54F15
DOI: https://doi.org/10.1090/S0002-9939-97-04088-4
MathSciNet review: 1422845
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Abstract: 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: paulb@mscs.mu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-04088-4
Keywords: Ultraproduct, ultracoproduct, generalized arc, co-elementary equivalence, co-elementary map
Received by editor(s): July 2, 1996
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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