4 papers
Characterising projective and weakly projective Boolean algebras by coherent Freese--Nation separations
Tomasz Kania, Andrzej Kucharski, Sławomir Turek
We isolate a coherent finite-separation strengthening of the Freese--Nation property and use it to characterise projective and weakly projective Boolean algebras. A Boolean algebra…
Homogeneity of profinite graphs
Wiesław Kubiś, Andrzej Kucharski, Sławomir Turek
Profinite graphs are inverse limits of sequences of nonempty finite graphs. There exists a ``generic'' graph $\Pe$ in this category, although its edge relation is rather poor: only…
On generic topological embeddings
Wiesław Kubiś, Andrzej Kucharski, Sławomir Turek
We show that an embedding of a fixed 0-dimensional compact space into the Čech--Stone remainder as a nowhere dense P-set is the unique generic limit, a special object in…
Supercompact minus compact is super
Taras Banakh, Zdzisław Kosztołowicz, Sławomir Turek
According to a folklore characterization of supercompact spaces, a compact Hausdorff space is supercompact if and only if it has a binary closed -network. This characterization…