Tightly packed families of sots
Topological spaces compact with respect to a set of filters
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there...
Towers of measurable functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
Transitive Properties of Ideals on Generalized Cantor Spaces
We compute transitive cardinal coefficients of ideals on generalized Cantor spaces. In particular, we show that there exists a null set such that for every null set we can find such that A ∪ (A+x) cannot be covered by any translation of B.
Two cases when and are equal
We deal with two cardinal invariants and give conditions on their equality using Shelah's pcf theory.