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Topology and its Applications 132 (2003) 221234 www.elsevier.com/locate/topol

Summary: Topology and its Applications 132 (2003) 221­234
On the topological classification of starlike bodies
in Banach spaces
Daniel Azagra a,
, Tadeusz Dobrowolski b,1
a Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense,
Madrid 28040, Spain
b Department of Mathematics, Pittsburg State University, Pittsburg, KA 66762, USA
Received 5 October 2001; received in revised form 4 September 2002
Starlike bodies are interesting in nonlinear analysis because they are strongly related to
polynomials and smooth bump functions, and their topological and geometrical properties are
therefore worth studying. In this note we consider the question as to what extent the known results
on topological classification of convex bodies can be generalized for the class of starlike bodies, and
we obtain two main results in this line, one which follows the traditional Bessaga­Klee scheme for
the classification of convex bodies (and which in this new setting happens to be valid only for starlike
bodies whose characteristic cones are convex), and another one which uses a new classification
scheme in terms of the homotopy type of the boundaries of the starlike bodies (and which holds
in full generality provided the Banach space is infinite-dimensional).


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


Collections: Mathematics