## Kingman, category and combinatorics (2009)

### BibTeX

@MISC{Bingham09kingman,category,

author = {N. H. Bingham and A. J. Ostaszewski},

title = {Kingman, category and combinatorics},

year = {2009}

}

### OpenURL

### Abstract

Kingman’s Theorem on skeleton limits –passing from limits as n! 1 along nh (n 2 N) for enough h> 0 to limits as t! 1 for t 2 R –is generalized to a Baire/measurable setting via a topological approach. Its affinity with a combinatorial theorem due to Kestelman and to Borwein and Ditor and another due to Bergelson, Hindman and Weiss is established. As applications, a theory of ‘rational’ skeletons akin to Kingman’s integer skeletons, and more appropriate to a measurable setting, is developed, and two combinatorial results in the spirit of van der Waerden’s celebrated theorem on arithmetic progressions are offered.