The space is not always a continuous image of
♣-like principles under CH
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.
The sizes of relatively compact -spaces
The relativization of Gryzlov’s theorem about the size of compact -spaces with countable pseudocharacter is false.
On matrix rapid filters
Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.
Splitting -covers
The authors give a ZFC example for a space with but not .
Two remarks on weaker connected topologies
It is shown that no generalized Luzin space condenses onto the unit interval and that the discrete sum of 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
Players ONE and TWO play the following game: In the nth inning ONE chooses a set from a prescribed family ℱ of subsets of a space X; TWO responds by choosing an open subset of X. The players must obey the rule that 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 -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...
Sequential continuity on dyadic compacta and topological groups
We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.
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