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A new approach to bounded linear operators on C(ω*)

Grzech M.

Czasopismo Techniczne. Nauki Podstawowe

2014

R. 111, z. 3-NP

5--8

We discuss recent results on the connection between properties of a given bounded linear operator of C(ω*) and topological properties of some subset of ω* which the operator determines. A family of closed subsets of ω*, which codes some properties of the operator is defined. An example of application of the method is presented.

Artykuł przedstawia metodę badania własności ograniczonego operatora liniowego na C(ω*) poprzez badanie własności pewnej rodziny domkniętych pozbiorów ω* wyznaczonej przez ten operator. Przedstawiony został przykład zastosowania tej metody w przypadku projekcji.

On the compactness and countable compactness of 2R in ZF

Keremedis K., Felouzis E., Tachtsis E.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 4

293-302

In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements "2R is countably compact" and "2R is compact".

Crowded and selective ultrafilters under the covering property axiom

Ciesielski K., Pawlikowski J.

Journal of Applied Analysis

2003

Vol. 9, nr 1

19-55

In the paper we formulate an axiom CPAgame prism, which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to ω 1 , while c = ω 2 : the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number u. We will also show that CPAgame prism, implies the existence of crowded and selective ultrafilters as well as nonselective P-points. In addition we prove that under CPAgame prism every selective ultrafilter is ω 1-generated. The paper finishes with the proof that CPAgame prism holds in the iterated perfect set model.