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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Projective Fraïssé limits and the pseudo-arc


Authors: Trevor Irwin and Slawomir Solecki
Journal: Trans. Amer. Math. Soc. 358 (2006), 3077-3096
MSC (2000): Primary 03C98, 54F15
Published electronically: February 20, 2006
MathSciNet review: 2216259
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Abstract: The aim of the present work is to develop a dualization of the Fraïssé limit construction from model theory and to indicate its surprising connections with the pseudo-arc. As corollaries of general results on the dual Fraïssé limits, we obtain Mioduszewski's theorem on surjective universality of the pseudo-arc among chainable continua and a theorem on projective homogeneity of the pseudo-arc (which generalizes a result of Lewis and Smith on density of homeomorphisms of the pseudo-arc among surjective continuous maps from the pseudo-arc to itself). We also get a new characterization of the pseudo-arc via the projective homogeneity property.


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Additional Information

Trevor Irwin
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801
Address at time of publication: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: tirwin@math.uiuc.edu

Slawomir Solecki
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801
Email: ssolecki@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03928-6
PII: S 0002-9947(06)03928-6
Keywords: Fra{\"\i}ss{\'e} limit, pseudo-arc
Received by editor(s): July 7, 2004
Published electronically: February 20, 2006
Additional Notes: The second author was partially supported by NSF grant DMS-0102254
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.