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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…