Coarse compactifications and controlled products

Autor:	Shin-ichi Oguni, Takamitsu Yamauchi, Tomohiro Fukaya
Rok vydání:	2018
Předmět:	Pure mathematics Generalization Gromov product General Topology (math.GN) Metric Geometry (math.MG) Construct (python library) Metric space Corona (optical phenomenon) Mathematics - Metric Geometry FOS: Mathematics Geometry and Topology Analysis Mathematics Mathematics - General Topology
DOI:	10.48550/arxiv.1810.08720
Popis:	We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space complements the space as a coarse compactification. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications. Comment: 22 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d26fdb6474062ae38f0d16d106ac9b71 Zobrazit plný text záznamu