N. D. Lebedeva, A. M. Petrunin, “All-set-homogeneous spaces”, Algebra i Analiz, 2023, Volume 35, Issue 3,Pages <nobr>52

Research Papers

All-set-homogeneous spaces

N. D. Lebedeva^ab, A. M. Petrunin^c

^a Saint Petersburg State University
^b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^c Math. Dept. PSU, University Park, PA 16802, USA

Abstract: A metric space is said to be all-set-homogeneous if any isometry between its subsets can be extended to an isometry of the whole space. We give a classification of a certain subclass of all-set-homogeneous length spaces.

Keywords: metric homogeneous spaces, metric foundations of geometry, universal trees, Urysohn universal space, isometry group.

Received: 24.09.2022