The space of probabilistic 1-Lipschitz maps View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-21

AUTHORS

Mohammed Bachir

ABSTRACT

We introduce and study the natural notion of probabilistic 1-Lipschitz maps. We use the space of all probabilistic 1-Lipschitz maps to give a new method for the construction of probabilistic metric completion (respectively of probabilistic invariant metric group completion). Our construction is of independent interest. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic invariant metric group can be endowed with a monoid structure. Next, we explicit the set of all invertible elements of this monoid and characterize probabilistic invariant complete Menger groups by the space of all probabilistic 1-Lipschitz maps in the spirit of the classical Banach–Stone theorem. More... »

PAGES

1-29

Journal

TITLE

Aequationes mathematicae

ISSUE

N/A

VOLUME

N/A

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00010-019-00641-0

DOI

http://dx.doi.org/10.1007/s00010-019-00641-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112918525


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