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POROSITY IN THE SPACE OF HÖLDER-FUNCTIONS

Abstract : Let (X, d) be a bounded metric space with a base point 0 X , (Y, •) be a Banach space and Lip α 0 (X, Y) be the space of all α-Hölderfunctions that vanish at 0 X , equipped with its natural norm (0 < α ≤ 1). Let 0 < α < β ≤ 1. We prove that Lip β 0 (X, Y) is a σ-porous subset of Lip α 0 (X, Y), if (and only if) inf{d(x, x ′) : x, x ′ ∈ X; x = x ′ } = 0 (i.e. d is non-uniformly discrete). A more general result will be given.
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Preprints, Working Papers, ...
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https://hal-paris1.archives-ouvertes.fr/hal-03222485
Contributor : Mohammed Bachir Connect in order to contact the contributor
Submitted on : Sunday, May 30, 2021 - 4:52:27 PM
Last modification on : Wednesday, June 2, 2021 - 3:42:04 AM

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  • HAL Id : hal-03222485, version 2
  • ARXIV : 2105.04849

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Mohammed Bachir. POROSITY IN THE SPACE OF HÖLDER-FUNCTIONS. 2021. ⟨hal-03222485v2⟩

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