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On Urysohn’s ℝ-Tree. / Berestovskii, V. N.

In: Siberian Mathematical Journal, Vol. 60, No. 1, 01.01.2019, p. 10-19.

Research output: Contribution to journal › Article › peer-review

Harvard

Berestovskii, VN 2019, 'On Urysohn’s ℝ-Tree', Siberian Mathematical Journal, vol. 60, no. 1, pp. 10-19. https://doi.org/10.1134/S0037446619010026

APA

Berestovskii, V. N. (2019). On Urysohn’s ℝ-Tree. Siberian Mathematical Journal, 60(1), 10-19. https://doi.org/10.1134/S0037446619010026

Vancouver

Berestovskii VN. On Urysohn’s ℝ-Tree. Siberian Mathematical Journal. 2019 Jan 1;60(1):10-19. doi: 10.1134/S0037446619010026

Author

Berestovskii, V. N. / On Urysohn’s ℝ-Tree. In: Siberian Mathematical Journal. 2019 ; Vol. 60, No. 1. pp. 10-19.

BibTeX

@article{405dc5120c314df4b4a1d33036168706,
title = "On Urysohn{\textquoteright}s ℝ-Tree",
abstract = "In the short note of 1927, Urysohn constructed the metric space R that is nowhere locally separable. There is no publication with indications that R is a (noncomplete) ℝ-tree that has valency c at each point. The author in 1989, as well as Polterovich and Shnirelman in 1997, constructed ℝ-trees isometric to R unaware of the paper by Urysohn. In this paper the author considers various constructions of the ℝ-tree R and of the minimal complete ℝ-tree of valency c including R, as well as the characterizations of ℝ-trees, their properties, and connections with ultrametric spaces.",
keywords = "boundary, four-point property, injective hull, left-invariant geodesic metric, submetry, ultrametric, ℝ-tree, R-tree",
author = "Berestovskii, {V. N.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1134/S0037446619010026",
language = "English",
volume = "60",
pages = "10--19",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "1",

}

RIS

TY - JOUR

T1 - On Urysohn’s ℝ-Tree

AU - Berestovskii, V. N.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In the short note of 1927, Urysohn constructed the metric space R that is nowhere locally separable. There is no publication with indications that R is a (noncomplete) ℝ-tree that has valency c at each point. The author in 1989, as well as Polterovich and Shnirelman in 1997, constructed ℝ-trees isometric to R unaware of the paper by Urysohn. In this paper the author considers various constructions of the ℝ-tree R and of the minimal complete ℝ-tree of valency c including R, as well as the characterizations of ℝ-trees, their properties, and connections with ultrametric spaces.

AB - In the short note of 1927, Urysohn constructed the metric space R that is nowhere locally separable. There is no publication with indications that R is a (noncomplete) ℝ-tree that has valency c at each point. The author in 1989, as well as Polterovich and Shnirelman in 1997, constructed ℝ-trees isometric to R unaware of the paper by Urysohn. In this paper the author considers various constructions of the ℝ-tree R and of the minimal complete ℝ-tree of valency c including R, as well as the characterizations of ℝ-trees, their properties, and connections with ultrametric spaces.

KW - boundary

KW - four-point property

KW - injective hull

KW - left-invariant geodesic metric

KW - submetry

KW - ultrametric

KW - ℝ-tree

KW - R-tree

UR - http://www.scopus.com/inward/record.url?scp=85065259399&partnerID=8YFLogxK

U2 - 10.1134/S0037446619010026

DO - 10.1134/S0037446619010026

M3 - Article

AN - SCOPUS:85065259399

VL - 60

SP - 10

EP - 19

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -

ID: 20039661