On the center of distances

0489402 - MÚ 2019 RIV DE eng J - Článek v odborném periodiku
Bielas, Wojciech - Plewik, S. - Walczyńska, Marta
On the center of distances.
European Journal of Mathematics. Roč. 4, č. 2 (2018), s. 687-698. ISSN 2199-675X
Grant CEP: GA ČR GF16-34860L
Institucionální podpora: RVO:67985840
Klíčová slova: Cantorval center of distances von Neumann's theorem * set of subsums
Obor OECD: Pure mathematics
https://link.springer.com/article/10.1007%2Fs40879-017-0199-4

We introduce the notion of a center of distances of a metric space and use it in a generalization of the theorem by John von Neumann on permutations of two sequences with the same set of cluster points in a compact metric space. This notion is also used to study sets of subsums of some sequences of positive reals, as well for some impossibility proofs. We compute the center of distances of the Cantorval, which is the set of subsums of the sequence ..., and for other related subsets of the reals.
Trvalý link: http://hdl.handle.net/11104/0283822