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♣-like principles under CH

Winfried Just — 2001

Fundamenta Mathematicae

Some relatives of the Juhász Club Principle are introduced and studied in the presence of CH. In particular, it is shown that a slight strengthening of this principle implies the existence of a Suslin tree in the presence of CH.

On matrix rapid filters

Winfried JustPeter Vojtáš — 1997

Fundamenta Mathematicae

Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.

Two remarks on weaker connected topologies

Phil DelaneyWinfried Just — 1999

Commentationes Mathematicae Universitatis Carolinae

It is shown that no generalized Luzin space condenses onto the unit interval and that the discrete sum of 1 copies of the Cantor set consistently does not condense onto a connected compact space. This answers two questions from [2].

Gδ -sets in topological spaces and games

Winfried JustMarion ScheepersJuris StepransPaul Szeptycki — 1997

Fundamenta Mathematicae

Players ONE and TWO play the following game: In the nth inning ONE chooses a set O n from a prescribed family ℱ of subsets of a space X; TWO responds by choosing an open subset T n of X. The players must obey the rule that O n O n + 1 T n + 1 T n for each n. TWO wins if the intersection of TWO’s sets is equal to the union of ONE’s sets. If ONE has no winning strategy, then each element of ℱ is a G δ -set. To what extent is the converse true? We show that:  (A) For ℱ the collection of countable subsets of X:   1. There are subsets...

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