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Banach-Mazur game played in partially ordered sets

100%

Kubiś W.

Banach Center Publications

2016

tom 108

nr 1

151-160

Concepts, definitions, notions, and some facts concerning the Banach-Mazur game are customized to a more general setting of partial orderings. It is applied in the theory of Fraïssé limits and beyond, obtaining simple proofs of universality of certain objects and classes.

A decomposition theorem for compact groups with an application to supercompactness

63%

Kubiś W. , Turek S.

nr 3

593-602

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.