A lower density operator for the Borel algebra

2019/02/26 by Marek Balcerzak, Balcerzak, Marek, Szymon Głab +1
Mathematics · #03E35 #FOS: Mathematics #General Topology (math.GN) #Primary: 28A51 #Secondary: 03E50 #math.GN #msc:03E35 #msc:03E50 #msc:28A51

paper · pdf · doi:10.48550/arxiv.1903.02397

arxiv created 2019/02/26 · arxiv updated 2019/11/04

Abstract

We prove that the existence of a Borel lower density operator (a Borel lifting) with respect to the σ-ideal of countable sets, for an uncountable Polish space, is equivalent to the Continuum Hypothesis.

Related

• Borel Conjecture for the Marczewski ideal
• Borel hierarchies in infinite products of Polish spaces
• Baire Category Lower Density Operators with Borel Values
• Abstract densities and ideals of sets
• Forcing properties of ideals of closed sets