Van der Waerden spaces and Hindman spaces are not the same
Abstract
A Hausdorff topological space X is van der Waerden if for every sequence (xn)n in X there is a converging subsequence (xn)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 (xn)n in X there is an IP-converging subsequence (xn)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.
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