Marczewski sets in the Hashimoto topologies for measure and category
Marczewski sets, measure and the Baire property
Measurability of equivalence classes and MEC-property in metric spaces.
Measurability of some sets of Borel measurable functions on .
Measurable functionals on function spaces
We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.
Measurable uniform spaces
Metric spaces admitting only trivial weak contractions
If (X,d) is a metric space then a map f: X → X is defined to be a weak contraction if d(f(x),f(y)) < d(x,y) for all x,y ∈ X, x ≠ y. We determine the simplest non-closed sets X ⊆ ℝⁿ in the sense of descriptive set-theoretic complexity such that every weak contraction f: X → X is constant. In order to do so, we prove that there exists a non-closed set F ⊆ ℝ such that every weak contraction f: F → F is constant. Similarly, there exists a non-closed set G ⊆ ℝ such that every weak contraction...
Metric spaces in which a strengthened form of Blumberg's theorem holds
Metric-fine, proximally fine, and locally fine uniform spaces
More Lusin properties in the product space
More on sg-compact spaces.
Multiapplications boréliennes à valeurs convexes de