On the topological classification of starlike bodies in Banach spaces



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Azagra Rueda, Daniel and Dobrowolski, Tadeusz (2003) On the topological classification of starlike bodies in Banach spaces. Topology and its Applications, 132 (3). pp. 221-234. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/journal/01668641


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 Bessaga-Klee 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).

Item Type:Article
Uncontrolled Keywords:Convex bodies; Manifolds; Smooth; Homeomorphisms; Negligibility; Spines; Starlike body; Homeomorphism
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:14502
Deposited On:01 Feb 2012 16:07
Last Modified:01 Feb 2012 16:27

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