Assouad dimensions of complementary sets

Autores
Garcia, Ignacio Andres; Hare, Kathryn; Mendivil, Franklin
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a positive, decreasing sequence a, whose sum is L, we consider all the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence a. The aim of this paper is to investigate the possible values that Assouad-type dimensions can attain for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine.
Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Hare, Kathryn. University of Waterloo; Canadá
Fil: Mendivil, Franklin. Acadia University; Canadá
Materia
ASSOUAD DIMENSION
COMPLEMENTARY SETS
CANTOR SETS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/89215
Acceder
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spelling Assouad dimensions of complementary setsGarcia, Ignacio AndresHare, KathrynMendivil, FranklinASSOUAD DIMENSIONCOMPLEMENTARY SETSCANTOR SETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a positive, decreasing sequence a, whose sum is L, we consider all the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence a. The aim of this paper is to investigate the possible values that Assouad-type dimensions can attain for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine.Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Hare, Kathryn. University of Waterloo; CanadáFil: Mendivil, Franklin. Acadia University; CanadáRoyal Society of Edinburgh2018-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/89215Garcia, Ignacio Andres; Hare, Kathryn; Mendivil, Franklin; Assouad dimensions of complementary sets; Royal Society of Edinburgh; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 148; 3; 7-2018; 517-5400308-2105CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0308210517000488info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/assouad-dimensions-of-complementary-sets/376B1D2E0F4BA421F74D69D1D7741B42info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:50Zoai:ri.conicet.gov.ar:11336/89215instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:47:50.519CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Assouad dimensions of complementary sets
title Assouad dimensions of complementary sets
spellingShingle Assouad dimensions of complementary sets
Garcia, Ignacio Andres
ASSOUAD DIMENSION
COMPLEMENTARY SETS
CANTOR SETS
title_short Assouad dimensions of complementary sets
title_full Assouad dimensions of complementary sets
title_fullStr Assouad dimensions of complementary sets
title_full_unstemmed Assouad dimensions of complementary sets
title_sort Assouad dimensions of complementary sets
dc.creator.none.fl_str_mv Garcia, Ignacio Andres
Hare, Kathryn
Mendivil, Franklin
author Garcia, Ignacio Andres
author_facet Garcia, Ignacio Andres
Hare, Kathryn
Mendivil, Franklin
author_role author
author2 Hare, Kathryn
Mendivil, Franklin
author2_role author
author
dc.subject.none.fl_str_mv ASSOUAD DIMENSION
COMPLEMENTARY SETS
CANTOR SETS
topic ASSOUAD DIMENSION
COMPLEMENTARY SETS
CANTOR SETS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a positive, decreasing sequence a, whose sum is L, we consider all the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence a. The aim of this paper is to investigate the possible values that Assouad-type dimensions can attain for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine.
Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Hare, Kathryn. University of Waterloo; Canadá
Fil: Mendivil, Franklin. Acadia University; Canadá
description Given a positive, decreasing sequence a, whose sum is L, we consider all the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence a. The aim of this paper is to investigate the possible values that Assouad-type dimensions can attain for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine.
publishDate 2018
dc.date.none.fl_str_mv 2018-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/89215
Garcia, Ignacio Andres; Hare, Kathryn; Mendivil, Franklin; Assouad dimensions of complementary sets; Royal Society of Edinburgh; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 148; 3; 7-2018; 517-540
0308-2105
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89215
identifier_str_mv Garcia, Ignacio Andres; Hare, Kathryn; Mendivil, Franklin; Assouad dimensions of complementary sets; Royal Society of Edinburgh; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 148; 3; 7-2018; 517-540
0308-2105
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1017/S0308210517000488
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/assouad-dimensions-of-complementary-sets/376B1D2E0F4BA421F74D69D1D7741B42
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Royal Society of Edinburgh
publisher.none.fl_str_mv Royal Society of Edinburgh
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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