22 citations · 105 across the 33 of their papers we have counts for
8 papers · 1 filter
Egorov ideals
Adam Kwela
We study Egorov ideals, that is ideals on for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological $\bf{Σ^…
New Hindman spaces
Rafał Filipów, Krzysztof Kowitz, Adam Kwela +1
We introduce a method that allows to turn topological questions about Hindman spaces into purely combinatorial questions about the Katětov order of ideals on . We also…
Characterizing existence of certain ultrafilters
Rafał Filipów, Krzysztof Kowitz, Adam Kwela
Following Baumgartner [J. Symb. Log. 60 (1995), no. 2], for an ideal on , we say that an ultrafilter on is an -ultrafilter if for ev…
Spaces not distinguishing ideal pointwise and -uniform convergence
Rafał Filipów, Adam Kwela
We examine topological spaces not distinguishing ideal pointwise and ideal -uniform convergence of sequences of real-valued continuous functions defined on them. For instance, w…
Yet another ideal version of the bounding number
Rafał Filipów, Adam Kwela
Let be an ideal on . For we write if for all with some . Moreover, we den…
A unified approach to Hindman, Ramsey and van der Waerden spaces
Rafał Filipów, Krzysztof Kowitz, Adam Kwela
For many years, there have been conducting research (e.g. by Bergelson, Furstenberg, Kojman, Kubiś, Shelah, Szeptycki, Weiss) into sequentially compact spaces that are, in a sense,…
Katětov order between Hindman, Ramsey, van der Waerden and summable ideals
Rafał Filipów, Krzysztof Kowitz, Adam Kwela
A family I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal I on X is below an ideal J on Y in the Katetov or…
The ideal test for the divergence of a series
Rafał Filipów, Adam Kwela, Jacek Tryba
We generalize the classical Olivier's theorem which says that for any convergent series with positive nonincreasing real terms the sequence tends to zero. Ou…