Assouad dimensions of complementary sets

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 dimens...

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Detalles Bibliográficos
Autores: Garcia, Ignacio Andres, Hare, Kathryn, Mendivil, Franklin
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/89215
Acceso en línea:http://hdl.handle.net/11336/89215
Access Level:acceso abierto
Palabra clave:ASSOUAD DIMENSION
COMPLEMENTARY SETS
CANTOR SETS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.