Metric trees in the Gromov--Hausdorff space
Commentationes Mathematicae Universitatis Carolinae (2023)
- Volume: 64, Issue: 1, page 73-82
- ISSN: 0010-2628
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topIshiki, Yoshito. "Metric trees in the Gromov--Hausdorff space." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 73-82. <http://eudml.org/doc/299454>.
@article{Ishiki2023,
abstract = {Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.},
author = {Ishiki, Yoshito},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {metric tree; Gromov--Hausdorff distance},
language = {eng},
number = {1},
pages = {73-82},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Metric trees in the Gromov--Hausdorff space},
url = {http://eudml.org/doc/299454},
volume = {64},
year = {2023},
}
TY - JOUR
AU - Ishiki, Yoshito
TI - Metric trees in the Gromov--Hausdorff space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 73
EP - 82
AB - Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.
LA - eng
KW - metric tree; Gromov--Hausdorff distance
UR - http://eudml.org/doc/299454
ER -
References
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