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GEOMETRY OF LINEAR AND NONLINEAR GEODESICS IN THE PROPER GROMOV--HAUSDORFF CLASSстатья
- Автор: Vikhrov Anton
- Журнал: Matematicki Vesnik
- Год издания: 2025
- Издательство: Drustvo Matematicara SR Srbije
- Местоположение издательства: Serbia
- DOI: 10.57016/mv-nsoc2660
- Аннотация: This paper investigates the proper class of all metric spaces considered up to isometry, equipped with the Gromov--Hausdorff distance. There constructed a pair of complete metric spaces, X and Y such that they have no metric spaces at zero distance, no optimal correspondence between X and Y, and therefore no linear geodesics joining them, but there exists a geodesic between them of a different type. There also described everywhere dense subclass of the Gromov--Hausdorff class such that any two points at finite distance within this subclass can be connected by a linear geodesic.
- Добавил в систему: Вихров Антон Андреевич