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| HAL: hal-00447814, version 1 |
| arXiv: 1001.3231 |
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| Cahiers de topologie et géométrie différentielle catégoriques XI, 2 (1969) 207-214 |
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| Une Structure Uniforme sur un Espace F(E,F) |
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| Nicolas Bouleau 1 |
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| (1969) |
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| Let E be a topological space and F a uniform space. We introduce a new topology (in fact a uniform structure) called the V-congergence on the space of applications from E to F such that C(E,F) is closed for this topology and the restriction of this topology to C(E,F) is equivalent to pointwise convergence. In other words this topology is the coarsest preserving continuity. We give a criterion of convergence for this topology not involving the limit. Among properties preserved are mesurability and alpha-borelianity for a countable ordinal alpha. |
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| 1: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Subject | : | Mathematics/General Topology |
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| continuity – neighborhood – Banach – compact |
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| hal-00447814, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00447814 | |
| oai:hal.archives-ouvertes.fr:hal-00447814 | |
| From: Nicolas Bouleau | |
| Submitted on: Tuesday, 19 January 2010 10:18:21 | |
| Updated on: Tuesday, 19 January 2010 10:28:25 | |
