On Effros continua and the uniform property of Effros

We recall a theorem by E. G. Effros about the actions of a separable complete metric group acting transitively on a complete metric space. We consider the definition, by D. P. Bellamy and K. F. Porter of an Effros continuum in the class of Hausdorff homogeneous continua. We also recall the definiti...

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Main Author: Sergio Macías
Format: Article
Language:Spanish
Published: Universidad Industrial de Santander 2025-07-01
Series:Revista Integración
Subjects:
Online Access:https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/16566
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author Sergio Macías
author_facet Sergio Macías
author_sort Sergio Macías
collection DOAJ
description We recall a theorem by E. G. Effros about the actions of a separable complete metric group acting transitively on a complete metric space. We consider the definition, by D. P. Bellamy and K. F. Porter of an Effros continuum in the class of Hausdorff homogeneous continua. We also recall the definition of the uniform property of Effros for Hausdorff continua. We prove that a homogeneous Hausdorff continuum is an Effros continuum if and only if it has the uniform property of Effros. We consider the weak property of Effros introduced by F. W. Simmons and show that Hausdorff continua with the weak property of Effros are homogeneous. We introduce the uniform weak property of Effros. We show that it is equivalent to the definition given by Simmons and that a Hausdorff continuum with the uniform property of Effros has uniform the weak property of Effros.
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spelling doaj-art-90abf65e2ee54c7c911a6eecb2fdcdc62025-08-20T02:57:48ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722025-07-01431On Effros continua and the uniform property of EffrosSergio Macías0Universidad Nacional Autónoma de México We recall a theorem by E. G. Effros about the actions of a separable complete metric group acting transitively on a complete metric space. We consider the definition, by D. P. Bellamy and K. F. Porter of an Effros continuum in the class of Hausdorff homogeneous continua. We also recall the definition of the uniform property of Effros for Hausdorff continua. We prove that a homogeneous Hausdorff continuum is an Effros continuum if and only if it has the uniform property of Effros. We consider the weak property of Effros introduced by F. W. Simmons and show that Hausdorff continua with the weak property of Effros are homogeneous. We introduce the uniform weak property of Effros. We show that it is equivalent to the definition given by Simmons and that a Hausdorff continuum with the uniform property of Effros has uniform the weak property of Effros. https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/16566Continuumdecomposable continuumEffros continuumHausdorff continuummetric continuumgroup action
spellingShingle Sergio Macías
On Effros continua and the uniform property of Effros
Revista Integración
Continuum
decomposable continuum
Effros continuum
Hausdorff continuum
metric continuum
group action
title On Effros continua and the uniform property of Effros
title_full On Effros continua and the uniform property of Effros
title_fullStr On Effros continua and the uniform property of Effros
title_full_unstemmed On Effros continua and the uniform property of Effros
title_short On Effros continua and the uniform property of Effros
title_sort on effros continua and the uniform property of effros
topic Continuum
decomposable continuum
Effros continuum
Hausdorff continuum
metric continuum
group action
url https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/16566
work_keys_str_mv AT sergiomacias oneffroscontinuaandtheuniformpropertyofeffros