Marek Balcerzak

Can ideals without ccc be interesting

Abstract We study those ideals I of sets in a perfect Polish space X which admit a Borel measurable f : X → X with f -1 [\s{ x \s}]∉ I for each x ϵ X . A stronger version of that property (when, additionally, X is a group and I an invariant ideal) states that there exist a Borel set B ∉ I and a perfect P ⊆ X , such that \s{ B + x : x ϵ P \s} forms a disjoint family.

COVERING PROPERTIES OF IDEALS

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices of the required subsequence should be in a fixed ideal

Local Extrema and Nonopenness Points of Continuous Functions

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Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

on ω. We introduce the notion of the

Nonseparable spaceability and strong algebrability of sets of continuous singular functions

{{\mathcal{J}}}

Some types of convergence and related Baire systems

-covering property of a pair