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2013 | OriginalPaper | Buchkapitel

3. Quantitative Metrization Theory

verfasst von : Dorina Mitrea, Irina Mitrea, Marius Mitrea, Sylvie Monniaux

Erschienen in: Groupoid Metrization Theory

Verlag: Birkhäuser Boston

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Abstract

This chapter contains our most general abstract results pertaining to the metrization of semigroupoids and groupoids equipped with quasisubadditive functions. Moreover, several metrization results in this setting with additional constraints are established. We explain how our results generalize the classic Aoki–Rolewicz theorem for quasinormed vector spaces and yield a sharp version of the Macías–Segovia metrization theorem for quasimetric spaces. An application to analytic capacity is also discussed, and connections with homogeneous groups are explored.

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Vorheriges Kapitel Semigroupoids and Groupoids
Nächstes Kapitel Applications to Analysis on Quasimetric Spaces
Fußnoten
1
The issue of proving metrization results in the spirit of the Aoki–Rolewicz theorem in the noncommutative context has been occasionally raised in other works, such as in [28, Problem 5.2, p. 47].
 
2
We became aware of this reference right after we had completed the present work.
 
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Metadaten
Titel
Quantitative Metrization Theory
verfasst von
Dorina Mitrea
Irina Mitrea
Marius Mitrea
Sylvie Monniaux
Copyright-Jahr
2013
Verlag
Birkhäuser Boston
Buch
Groupoid Metrization Theory

Print ISBN: 978-0-8176-8396-2

Electronic ISBN: 978-0-8176-8397-9

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-0-8176-8397-9_3