The Lelek fan and the Poulsen simplex as Fra\"iss\'e limits
General Topology
2016-12-20 v3 Functional Analysis
Abstract
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 Fra\"{i}ss\'e 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.
Keywords
Cite
@article{arxiv.1512.09252,
title = {The Lelek fan and the Poulsen simplex as Fra\"iss\'e limits},
author = {Wiesław Kubiś and Aleksandra Kwiatkowska},
journal= {arXiv preprint arXiv:1512.09252},
year = {2016}
}
Comments
version accepted to RACSAM