Infinitesimal bi-Lipschitz Equivalence of Functions
Terence Gaffney
TL;DR
This paper introduces two notions of infinitesimal bi-Lipschitz equivalence for functions, analyzing their genericity and relation to bi-Lipschitz triviality and fiber homeomorphisms.
Contribution
It defines and compares two new concepts of infinitesimal bi-Lipschitz equivalence, establishing their properties and genericity.
Findings
The first notion is not a generic condition.
The second notion is a generic condition.
Both notions relate to bi-Lipschitz triviality and fiber homeomorphisms.
Abstract
We introduce two different notions of infinitesimal bi-Lipschitz equivalence for functions, one related to bi-Lipschitz triviality of families of functions, one related to homeomorphisms which are bi-Lipschitz on the fibers of the functions in the family. We show that the first is not a generic condition, and that the second is.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Advanced Topology and Set Theory · Optimization and Variational Analysis