Van der Waerden spaces and Hindman spaces are not the same
General Topology
2007-05-23 v1 Logic
Abstract
A Hausdorff topological space X is van der Waerden if for every sequence (x_n)_n in X there is a converging subsequence (x_n)_{n in A} where subset A of omega contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (x_n)_n in X there is an IP-converging subsequence (x_n)_{n in FS(B)} for some infinite subset B of omega. We show that the continuum hypothesis implies the existence of a van der Waerden space which is not Hindman.
Keywords
Cite
@article{arxiv.math/0112265,
title = {Van der Waerden spaces and Hindman spaces are not the same},
author = {Menachem Kojman and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0112265},
year = {2007}
}