On the category of profinite spaces as a reflective subcategory
[EN] In this paper by using the ring of real-valued continuous functions C(X), we prove a theorem in profinite spaces which states that for a compact Hausdorff space X, the set of its connected components X/~ endowed with the quotient topology is a profinite space. Then we apply this result to give...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/32888 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/32888 |
| Access Level: | acceso abierto |
| Palabra clave: | Profinite spaces Coarser topology, Connected components Reflective subcategory |
| Sumario: | [EN] In this paper by using the ring of real-valued continuous functions C(X), we prove a theorem in profinite spaces which states that for a compact Hausdorff space X, the set of its connected components X/~ endowed with the quotient topology is a profinite space. Then we apply this result to give an alternative proof to the fact that the category of profinite spaces is a reflective subcategory in the category of compact Hausdorff spaces. Finally, under some circumstances on a space X, we compute the connected components of the space t(X) in terms of the ones of the space X. |
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