Marczewski sets in the Hashimoto topologies for measure and category
Marek Balcerzak, Joanna Rzepecka (1998)
Acta Universitatis Carolinae. Mathematica et Physica
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Marek Balcerzak, Joanna Rzepecka (1998)
Acta Universitatis Carolinae. Mathematica et Physica
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Marek Balcerzak (1986)
Mathematica Slovaca
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Petr Holický, Luděk Zajíček, Miroslav Zelený (2005)
Commentationes Mathematicae Universitatis Carolinae
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S. Solecki proved that if is a system of closed subsets of a complete separable metric space , then each Suslin set which cannot be covered by countably many members of contains a set which cannot be covered by countably many members of . We show that the assumption of separability of cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the -ideal generated by is locally determined. Using Solecki’s arguments, our result...
Dušan Holý, Peter Vadovič (2008)
Czechoslovak Mathematical Journal
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We consider the space of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of and investigate the subspace of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence . The largest part of the paper is devoted to the study of various cardinal functions for , in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, -weight,...