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E extracta mathematicae Vol. 19, Num. 2, 171 213 (2004) Starlike Bodies and Deleting Diffeomorphisms in

Summary: E extracta mathematicae Vol. 19, N´um. 2, 171 ­ 213 (2004)
Starlike Bodies and Deleting Diffeomorphisms in
Banach Spaces
Daniel Azagra, Alejandro Montesinos
Departamento de An´alisis Matem´atico, Facultad de Ciencias Matem´aticas,
Universidad Complutense, 28040 Madrid, Spain
e-mail: daniel azagra@mat.ucm.es, a montesinos@mat.ucm.es
(Presented by Jes´us A. Jaramillo)
AMS Subject Class. (2000): 46B20, 57R50, 58B99 Received July 9, 2003
1. Introduction
A subset K of X is said to be topologically negligible provided there exists
a homeomorphism h : X X \K. The homeomorphism h is usually required
to be the identity outside a given neighborhood U of K. Here X can be
a Banach space, a manifold, or just a topological space, but we will only
consider the case when X is an infinite-dimensional Banach space and h is
a diffeomorphism (recall that points are not topologically negligible in finite-
dimensional spaces). Such h will be called a deleting diffeomorphism, and we
will say that h has its support on U.
Deleting diffeomorphisms are very powerful tools in infinite-dimensional
global analysis and nonlinear analysis. We do not intend to make a history of


Source: Azagra Rueda, Daniel - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid


Collections: Mathematics