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Quasi topology and fine topology

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  • Mathematics


Quasi topology and fine topology Séminaire Brelot-Choquet-Deny. Théorie du potentiel BENT FUGLEDE Quasi topology and fine topology Séminaire Brelot-Choquet-Deny. Théorie du potentiel, tome 10, no 2 (1965-1966), exp. no 12, p. 1-14. <> © Séminaire Brelot-Choquet-Deny. Théorie du potentiel (Secrétariat mathématique, Paris), 1965-1966, tous droits réservés. L’accès aux archives de la collection « Séminaire Brelot-Choquet-Deny. Théorie du potentiel » implique l’accord avec les conditions générales d’utilisation ( Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques 12-01 QUASI TOPOLOGY AND FINE TOPOLOGY Bent FUGLEDE Séminaire BRELOT-CHOQDET-DENY (Théorie du Potential) lOe 1965/~6~ t n° 12 5,12 et20mai 1966 Introduction. - When a subadditive capacity is gjven on a space , one may study quasi topological notions such as quasi closed sets, quasi continuous functions, etc. (cf. [8]). The results obtained are analogous to those for the fine topology in classical cases. Under suitable assumptions the quasi topology is shown to be equivalent to the fine topology, as is well known in classical potential theory. In case of the usual capacity with respect to a kernel, we establish this key result under the principal hypothesis of a dilated domination principle which is fulfilled, e. g. by the kernels of order a for all a . Some of the results of the present report were announced in [9~ 1. Quasi topology. - Let X denote a Hausdorff space, and c capacit on X in the sense of CHOQUET [3]~ defined for all compact subsets of X and with values in (0 , + oo) . Let c be the associated outer capacity, defined for arbitrary sub- sets of X . We assume that

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