Inverse Systems and I-Favorable Spaces

A compact space X is I-favorable if, and only if X can be representing as a limit of $\sigma$-complete inverse system of compact metrizable spaces with skeletal bonding maps.Comment: 13 page

Cardinal invariants for C-cross topologies

C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam Theorem are considered. Cardinal invariants add, cof, cov and non with respect to meager or nowhere dense subsets are compared. Remarks on invariants cof(nwdY) are mentioned for dense subspaces Y of X.Comment: 11 page

Hausdorff gaps reconstructed from Luzin gaps

We consider a question: Can a given AD-family be ADR for two orthogonal uncountable towers? If $b > \omega_1$, then we rebuilt any AD-family of the cardinality $\omega_1$ onto a Hausdorff pre-gap. Moreover, if a such AD-family is a Luzin gap, then we obtain a Hausdorff gap. Under $b = \omega_1$, a similar rebuilding is impossible.Comment: 7 page

Ideals which generalize (v0)(v^0)

We consider ideals $d^0(\mathcal{V})$ which are generalizations of the ideal $(v^0)$. We formulate couterparts of Hadamard's theorem. Then, adopting the base tree theorem and applying Kulpa-Szyma\'nski Theorem, we obtain $cov(d^0(\mathcal{V}))\leq add(d^0(\mathcal{V}))^+$.Comment: A part of Kalemba's dissertation, under Plewik's supervision, is contained her

A theorem on spaces of finite subsets

We give conditions under which iterated hyperspaces of finite subsets, with Ochan’s topology, are homeomorphic