Atlas: Descriptive set-theoretical properties of an abstract density operator by Szymon Glab

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Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland

Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis

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Descriptive set-theoretical properties of an abstract density operator
by
Szymon Głab
Institute of Mathematics, Technical University of \Lódź

Let K(R) stand for the hyperspace of all nonempty compact sets on the real line and let d^±(x, E) denote the (right- or left-hand) Lebesgue density of a measurable set E ⊂ R at a point x ∈ R. In my PhD thesis (defended in Nov, 2007) it was proved that

{K ∈ K(R):∀x ∈ K(d⁺(x, K)=1 or d^-(x, K)=1)}

is \pmb P¹₁-complete. I define an abstract density operator D^± and generalize the above result. Some applications will be given.

A full version of the paper is available on http://im0.p.lodz.pl/ sglab/szymon/absDeng.pdf

Date received: June 30, 2008