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.
Original language | English (US) |
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Pages (from-to) | 3077-3096 |
Number of pages | 20 |
Journal | Transactions of the American Mathematical Society |
Volume | 358 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2006 |
Keywords
- Fraïssé limit
- Peeudo-arc
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics