The universal minimal flow of the homeomorphism group of the Lelek fan

DOI10.1090/tran/7548zbMath1410.05216arXiv1706.09154OpenAlexW2963588343WikidataQ130158741 ScholiaQ130158741MaRDI QIDQ4633769

Dana Bartošová, Aleksandra Kwiatkowska

Publication date: 6 May 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.09154

zbMATH Keywords

Fraïssé limitsdual Ramsey theoremuniversal minimal flowshomeomorphism group of the Lelek an

Mathematics Subject Classification ID

Continua and generalizations (54F15) Ramsey theory (05D10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Applications of model theory (03C98)

Related Items (4)

Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable ⋮ Universal minimal flows of extensions of and by compact groups ⋮ Fences, their endpoints, and projective Fraïssé theory ⋮ Fixed points in compactifications and combinatorial counterparts

Cites Work

• The Ramsey property for Banach spaces and Choquet simplices, and applications
• Minimal actions of the group \(\mathbb{S}(\mathbb{Z})\) of permutations of the integers
• Gowers' Ramsey theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan
• Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups
• Topological dynamics of automorphism groups, ultrafilter combinatorics, and the Generic Point Problem
• More on the Kechris–Pestov–Todorcevic correspondence: Precompact expansions
• On plane dendroids and their end points in the classical sense
• Projective Fraïssé limits and the pseudo-arc
• On free actions, minimal flows, and a problem by Ellis
• The universal minimal system for the group of homeomorphisms of the Cantor set
• A Characterization of Smooth Cantor Bouquets
• Lelek fan from a projective Fraïssé limit
• Ramsey's Theorem for n-Parameter Sets
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