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p-adic Ascoli theorems.

Javier Martínez-Maurica, S. Navarro (1990)

Revista Matemática de la Universidad Complutense de Madrid

The aim of this paper is the study of a certain class of compact-like sets within some spaces of continuous functions over non-Archimedean ground fields. As a result, some p-adic Ascoli theorems are obtained.

P-adic Spaces of Continuous Functions I

Athanasios Katsaras (2008)

Annales mathématiques Blaise Pascal

Properties of the so called θ o -complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space C ( X , E ) of all continuous functions, from a zero-dimensional topological space X to a non-Archimedean locally convex space E , equipped with the topology of uniform convergence on the compact subsets of X to be polarly barrelled or polarly quasi-barrelled.

Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces

Alexander V. Abanin, Pham Trong Tien (2012)

Studia Mathematica

We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional.

P-convexity of Musielak-Orlicz function spaces of Bochner type.

Pawel. Kolwicz, Ryszard Pluciennik (1998)

Revista Matemática Complutense

It is proved that the Musielak-Orlicz function space LF(mu,X) of Bochner type is P-convex if and only if both spaces LF(mu,R) and X are P-convex. In particular, the Lebesgue-Bochner space Lp(mu,X) is P-convex iff X is P-convex.

Perfect sets of finite class without the extension property

A. Goncharov (1997)

Studia Mathematica

We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.

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