The Lelek fan and the Poulsen simplex as Fraissé limits

0477378 - MÚ 2018 RIV ES eng J - Journal Article
Kubiś, Wieslaw - Kwiatkowska, A.
The Lelek fan and the Poulsen simplex as Fraissé limits.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 111, č. 4 (2017), s. 967-981. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA ČR(CZ) GAP201/12/0290
Institutional support: RVO:67985840
Keywords : Lelek fan * smooth fan * Fraissé limit
OECD category: Pure mathematics
Impact factor: 1.074, year: 2017
https://link.springer.com/article/10.1007%2Fs13398-016-0339-6

We describe the Lelek fan, a smooth fan whose set of end-points is dense, and the Poulsen simplex, a Choquet simplex whose set of extreme points is dense, as Fraissé limits in certain natural categories of embeddings and projections. As an application we give a short proof of their uniqueness, universality, and almost homogeneity. We further show that for every two countable dense subsets of end-points of the Lelek fan there exists an auto-homeomorphism of the fan mapping one set onto the other. This improves a result of Kawamura, Oversteegen, and Tymchatyn from 1996.
Permanent Link: http://hdl.handle.net/11104/0273742