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Ordinal ultrafilters versus P-hierarchy

Andrzej Starosolski — 2014

Open Mathematics

An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.

Extension of multisequences and countably uniradial classes of topologies

Szymon DoleckiAndrzej StarosolskiStephen W. Watson — 2003

Commentationes Mathematicae Universitatis Carolinae

It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter on ω , the class of -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....

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