---
res:
bibo_abstract:
- We consider infinite-dimensional properties in coarse geometry for hyperspaces
consisting of finite subsets of metric spaces with the Hausdorff metric. We see
that several infinite-dimensional properties are preserved by taking the hyperspace
of subsets with at most n points. On the other hand, we prove that, if a metric
space contains a sequence of long intervals coarsely, then its hyperspace of finite
subsets is not coarsely embeddable into any uniformly convex Banach space. As
a corollary, the hyperspace of finite subsets of the real line is not coarsely
embeddable into any uniformly convex Banach space. It is also shown that every
(not necessarily bounded geometry) metric space with straight finite decomposition
complexity has metric sparsification property.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Thomas
foaf_name: Weighill, Thomas
foaf_surname: Weighill
- foaf_Person:
foaf_givenName: Takamitsu
foaf_name: Yamauchi, Takamitsu
foaf_surname: Yamauchi
- foaf_Person:
foaf_givenName: NicolĂ˛
foaf_name: Zava, NicolĂ˛
foaf_surname: Zava
foaf_workInfoHomepage: http://www.librecat.org/personId=c8b3499c-7a77-11eb-b046-aa368cbbf2ad
orcid: 0000-0001-8686-1888
bibo_doi: 10.1007/s40879-021-00515-3
bibo_issue: '1'
bibo_volume: 8
dct_date: 2022^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/2199-675X
- http://id.crossref.org/issn/2199-6768
dct_language: eng
dct_publisher: Springer Nature@
dct_title: Coarse infinite-dimensionality of hyperspaces of finite subsets@
...