### van der Waerden spaces and Hindman spaces are not the same

by Kojman and Shelah. [KjSh:781]

Proc American Math Soc, 2003

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 A subseteq 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 B subseteq omega .
We show that the continuum hypothesis implies the existence of a van
der Waerden space which is not Hindman.

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