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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| Language: | Spanish |
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Universidad Industrial de Santander
2025-07-01
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| Series: | Revista Integración |
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| 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 |
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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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| format | Article |
| id | doaj-art-90abf65e2ee54c7c911a6eecb2fdcdc6 |
| institution | DOAJ |
| issn | 0120-419X 2145-8472 |
| language | Spanish |
| publishDate | 2025-07-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista Integración |
| 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 |