Centre of Distances of a Subset of the Real Line

28.06.2021 - 02.07.2021 | Będlewo

The scope of the meeting:

The notion of a center of distances was introduced in [BPW]. This interesting invariant of a metric space is a handy tool to check whether a subset of reals is an achievement set of some sequence. This problem have recently been extensively studied (see for example [BGM], [BBP] and [BP]).
A. Bartoszewicz, M. Filipczak and F. Prus-Wiśniowski have been dealing with achievement sets for several years. Some their results have been published in [BFP], [BFP2], [BGFP] and [BBFS]. Centers of distances seems to be useful in testing achievement sets generating by semi-fast convergent sequences studied in [BFP2].

This year G. Horbaczewska with S. Lindner began to research centers of distances of compact subsets of the unit interval. In particular, they discuss properties of the function transforming compact sets to its centers of distances.
We plan to characterize centers of distances of some class of central Cantor sets. We also intend to investigate centers of distances of other interesting subsets of the line. Possibility of direct contact between F. Prus-Wiśniowski and other members of the research group will improve our cooperation. We hope to use the methods and results of G. Horbaczewska to look at the distance center issue more broadly.

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