Year: 2015
Type: preprint
Abstract: We study transversality for Lipschitz-Fredholm maps in the context of bounded Fréchet manifolds. We show that the set of all Lipschitz-Fredholm maps of a fixed index between Fréchet spaces has the transverse stability property. We give a straightforward extension of the Smale transversality theorem by using the generalized Sard's theorem for this category of manifolds. We also provide an answer to the well known problem concerning the existence of a submanifold structure on the preimage of a transversal submanifold.
Source: arXiv (Cornell University)
Author: Eftekharinasab, Kaveh
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1837397490