Projective Fraïssé limits and the pseudo-arc

Trevor Irwin, Slawomir Solecki

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)3077-3096
Number of pages20
JournalTransactions of the American Mathematical Society
Volume358
Issue number7
DOIs
StatePublished - Jul 2006

Keywords

  • Fraïssé limit
  • Peeudo-arc

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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