Combinatorics of Open Covers (I): Ramsey Theory
NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. The definitive version has been published in Topology and its Applications, 69, 1, 1996, DOI: 10.1016/0166-8641(95)00067-4.
We study several schemas for generating from one sort of open cover of a topological space a second sort of open cover. Some of these schemas come from classical literature, others are borrowed from the theory of ultraﬁlters on the set of positive integers. We show that the fact that such a schema actually succeeds in producing a cover imposes strong combinatorial structure on the family of open covers of a certain sort. In particular, we show that certain analogues of Ramsey’s theorem characterize some of these circumstances.
Marion Scheepers. "Combinatorics of Open Covers (I): Ramsey Theory" Topology and its Applications 69.1 (1996): 31-62.
Available at: http://works.bepress.com/marion_scheepers/7