Van der Waerden spaces and Hindman spaces are not the same

Menachem Kojman, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A Hausdorff topological space X is van der Waerden if for every sequence (xn)n∈w in X there is a converging subsequence (xn)n∈A where A ⊆ w contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (xn)n∈w in X there is an IP-converging subsequence (xn)n∈FS(B) for some infinite B ⊆ w. We show that the continuum hypothesis implies the existence of a van der Waerden space which is not Hindman.

Original languageEnglish
Pages (from-to)1619-1622
Number of pages4
JournalProceedings of the American Mathematical Society
Volume131
Issue number5
DOIs
StatePublished - 1 May 2003

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