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Preprints, Working Papers, ... Year : 2021

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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Dates and versions

hal-03222485 , version 1 (10-05-2021)
hal-03222485 , version 2 (30-05-2021)

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