On the topological classification of starlike bodies in Banach spaces

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 cl...

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Detalhes bibliográficos
Autores: Azagra Rueda, Daniel, Dobrowolski, Tadeusz
Formato: artículo
Fecha de publicación:2003
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/49794
Acesso em linha:https://hdl.handle.net/20.500.14352/49794
Access Level:acceso abierto
Palavra-chave:517.98
Convex bodies
Manifolds
Smooth
Homeomorphisms
Negligibility
Spines
Starlike body
Homeomorphism
Análisis matemático
1202 Análisis y Análisis Funcional
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spelling On the topological classification of starlike bodies in Banach spacesAzagra Rueda, DanielDobrowolski, Tadeusz517.98Convex bodiesManifoldsSmoothHomeomorphismsNegligibilitySpinesStarlike bodyHomeomorphismAnálisis matemático1202 Análisis y Análisis FuncionalStarlike 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).Elsevier ScienceUniversidad Complutense de Madrid20032003-08-1520032003-08-15journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/49794reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/497942026-06-02T12:44:21Z
dc.title.none.fl_str_mv On the topological classification of starlike bodies in Banach spaces
title On the topological classification of starlike bodies in Banach spaces
spellingShingle On the topological classification of starlike bodies in Banach spaces
Azagra Rueda, Daniel
517.98
Convex bodies
Manifolds
Smooth
Homeomorphisms
Negligibility
Spines
Starlike body
Homeomorphism
Análisis matemático
1202 Análisis y Análisis Funcional
title_short On the topological classification of starlike bodies in Banach spaces
title_full On the topological classification of starlike bodies in Banach spaces
title_fullStr On the topological classification of starlike bodies in Banach spaces
title_full_unstemmed On the topological classification of starlike bodies in Banach spaces
title_sort On the topological classification of starlike bodies in Banach spaces
dc.creator.none.fl_str_mv Azagra Rueda, Daniel
Dobrowolski, Tadeusz
author Azagra Rueda, Daniel
author_facet Azagra Rueda, Daniel
Dobrowolski, Tadeusz
author_role author
author2 Dobrowolski, Tadeusz
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.98
Convex bodies
Manifolds
Smooth
Homeomorphisms
Negligibility
Spines
Starlike body
Homeomorphism
Análisis matemático
1202 Análisis y Análisis Funcional
topic 517.98
Convex bodies
Manifolds
Smooth
Homeomorphisms
Negligibility
Spines
Starlike body
Homeomorphism
Análisis matemático
1202 Análisis y Análisis Funcional
description 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).
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-08-15
2003
2003-08-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/49794
url https://hdl.handle.net/20.500.14352/49794
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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