On compact weaker topologies in function spaces
In this paper we prove that for every cardinal kappa, the space C-p(D-k) admits a continuous bijection onto a space whose all finite powers are Lindelof (the symbol D stands for the discrete two-point space). We also prove that for every metrizable compact space X, the space Cp (X) can be condensed...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2001 |
| 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:11154/1946 |
| Acceso en línea: | http://hdl.handle.net/11154/1946 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics, Applied Mathematics function spaces condensation topology of pointwise convergence weaker topologies |
| Sumario: | In this paper we prove that for every cardinal kappa, the space C-p(D-k) admits a continuous bijection onto a space whose all finite powers are Lindelof (the symbol D stands for the discrete two-point space). We also prove that for every metrizable compact space X, the space Cp (X) can be condensed (i.e., admits a continuous bijection) onto the Hilbert cube I-omega. As a consequence it is established that the space Cp (DI) can be condensed onto a compact space. In connection to this result, we also prove that there exist models of ZFC in which the statement "The spaces C-p(D-k) can be condensed onto a compact space for every cardinal kappa > omega" is not true. We show also that for every cardinal K, the spaces C-p(C-p(D-k)) and L-p(D-k) have dense subsets of countable tightness. (C) 2001 Elsevier Science B.V. All rights reserved. |
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