Ramsey limits and discrete selections
by
Dona Strauss
University of Hull
Coauthors: T.Carlson and N.Hindman

It is, of course, trivial that, for any mapping f from N to a Hausdorff space, there is an infinite subset A of N for which f[A] is discrete. I shall discuss the following question: which spaces X have the property that that, for any positive integer n and any mapping f from Nⁿ to X, there is an infinite subset A of N for which f[Aⁿ] is discrete? We have shown that this is a class which includes all F-spaces and their finite products.

Date received: June 14, 2004