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Remarks on some special points in extremally disconnected compact spaces
Joanna Jureczko
We prove under ZFC that in each extremally disconnected compact space there exists a non-limit point of any countable discrete subset.
Weak -points for regulars
Joanna Jureczko
The main result of this paper is to show that for any compact space and any family of open mappings ther…
On equivalences of polarized partition relations
Joanna Jureczko
The paper deals with two notions: polarized partition relations and product of generalized strong sequences. Strong sequences were introduced by Efimov in 1965 as a usefull tool fo…
Some remarks on polarized partition relations
Joanna Jureczko
This paper deals with two notions: a polarized partition relations and…
Ultrafilters without immediate predecessors in Rudin-Frolik order for regulars
Joanna Jureczko
The aim of this paper is to construct ultrafilters without immediate predecessors in the Rudin-Frolik order in , where is a regular cardinal. This generalizes th…
Chains in Rudin-Frolik order for regulars
Joanna Jureczko
The aim of this paper is to construct chains of length in the sense of Rudin-Frolík order in for regular.
A note on special subsets of the Rudin-Frolík order for regulars
Joanna Jureczko
We show that there is a set of ultrafilters incomparable in Rudin-Frolík order of , where is regular, for which no subset with more than one element ha…
Decreasing chains without lower bounds in Rudin-Frolík order for regulars
Joanna Jureczko
The aim of this paper is to prove that for there exist a chain in the Rudin-Frolík order of of length with for regular withou…
On some generalizations of the Halpern-Läuchli theorem
Joanna Jureczko
In this paper, several generalizations of the classical Halpern-Läuchli Theorem are proven for Marczewski and Ellentuck structures using only combinatorial methods.
Partitions and point-finite covers of Baire spaces
Joanna Jureczko
In this paper we show that the existence of Kuratowski partitions of Hausdorff Baire space is equivalent to the existence of point-finite covers of the same space.
Nonmeasurable sets in tree structures and Ellentuck topology
Joanna Jureczko
The aim of this paper is to provide the results that answer the Kuratowski problem posed in 1935 concerning the existence of nonmeasurable sets. The Kuratowski problem was consider…
A note on Kuratowski partitions in metric spaces
Joanna Jureczko
We prove that the existence of a complete metric space of cardinality at most admitting Kuratowski partition is a consequence of being the smallest real-valued measurable…