Projective Fraïssé limits and the pseudo-arc
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- by Trevor Irwin and Sławomir Solecki PDF
- Trans. Amer. Math. Soc. 358 (2006), 3077-3096 Request permission
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.References
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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
- Sławomir Solecki
- Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801
- Email: ssolecki@math.uiuc.edu
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 3077-3096
- MSC (2000): Primary 03C98, 54F15
- DOI: https://doi.org/10.1090/S0002-9947-06-03928-6
- MathSciNet review: 2216259