Projective Fraïssé limits and the pseudo-arc

By Trevor L. Irwin, Slawomir Solecki. 2006

78 citations recorded by the source corpus.

The aim of the present work is to develop a dualization of the Fraisse limit construction from model theory and to indicate its surprising connections with the pseudo-arc. As corollaries of general results on the dual Fraisse 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/37f2752d9616341ea4155c273d1f4d30c0a65b7d

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In Geometry and Topology

1. I. Yaacov
2. Todor Tsankov
3. Rostislav I. Grigorchuk

In Mathematical Physics

1. I. Yaacov
2. Todor Tsankov
3. Rostislav I. Grigorchuk

Citations in the corpus

• Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups (2013, methodology): “es to Homeo+([0,1])(with H =Aut(Q)), thus providing a new proof of Megrelishvili’s result, but also to some other homeomorphism groups. For example, using the method of projective Fraïssé limits (see [IS]), Bartošova and Kwiatkowska [BK] construct a homomorphism from a Roelcke precompact closed subg”