Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1422845
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03C20, 54B35, 54C10, 54D05, 54D30, 54D80, 54F05, 54F15

Retrieve articles in all journals with MSC (1991): 03C20, 54B35, 54C10, 54D05, 54D30, 54D80, 54F05, 54F15


Additional Information

Paul Bankston
Affiliation: Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53201-1881
Email: paulb@mscs.mu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04088-4
PII: S 0002-9939(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