Extensions of functions in Mrowka-Isbell spaces
For an almost disjoint family (a.d.f.) Sigma of subsets of omega, let Psi(Sigma) be the Mrowka-Isbell space on Sigma. In this article we will analyze the following problem: given an a.d.f. Sigma and a function phi:Sigma --> {0: 1} (respectively phi:Sigma --> R) is it possible to extend phi con...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1997 |
| País: | México |
| Institución: | Universidad Nacional Autónoma de México |
| Repositorio: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/2831 |
| Acceso en línea: | http://hdl.handle.net/11154/2831 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics, Applied Mathematics Mrowka-Isbell space almost disjoint family essential extension full extension arrow omega(1)-p-ultrafilter Martin's Axiom Cohen real Luzin gap Booth's Lemma |
| Sumario: | For an almost disjoint family (a.d.f.) Sigma of subsets of omega, let Psi(Sigma) be the Mrowka-Isbell space on Sigma. In this article we will analyze the following problem: given an a.d.f. Sigma and a function phi:Sigma --> {0: 1} (respectively phi:Sigma --> R) is it possible to extend phi continuously to a big enough subspace Sigma boolean OR N of Psi(Sigma) for which cl(Psi(Sigma)) N superset of Sigma? Such an extension is called essential. We will prove that: (i) for every a.d.f. Sigma of cardinality 2(N0) we can find a function phi:Sigma --> {0, I} without essential extensions |
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