Remarks on vector sums of Borel sets

On Vector Sums of Measure Zero Sets

We consider the behaviour of measure zero subsets of a vector space under the operation of vector sum. The question whether the vector sum of such sets can be nonmeasurable is discussed in connection with the measure extension problem, and a certain generalization of the classical Sierpiński result [3] is presented. 2000 Mathematics Subject Classification: 28A05, 28D05.

on direct sums of baer modules

the notion of baer modules was defined recently

A Course on Borel Sets

On monotone presentations of Borel sets

If A is a Σξ set and An (n < ω) are Borel sets then we call {An : n < ω} a presentation of A if A = S n<ω An and An (n < ω) have lower Borel class than A has. We show that for 2 ≤ ξ < ω1 it is not possible to assign a presentation to Σξ sets in a monotone way, i.e., it is not possible to define functions fn : Σ 0 ξ → Πξ (n < ω) such that for every A ∈ Σξ we have A = S n<ω fn(A) and A,A ′ ∈ Σξ, ...

On open maps of Borel sets

We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers P not Gδ · Fσ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ P of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. T...