Properties of the normed cone of semi-Lipschitz functions

Authors: Romaguera, Salvador¹; Sanchis, Manuel²

Source: Acta Mathematica Hungarica, Volume 108, Numbers 1-2, July 2005 , pp. 55-70(16)

Publisher: Springer

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Abstract:

<Para OutputMedium="All">We obtain several properties of the normed cone of semi-Lipschitz functions defined on a quasi-metric space (X,d) that vanish at a fixed point x₀ isin

x. For instance, we prove that it is both bicomplete and right K-sequentially complete, and the unit ball is compact with respect to the topology of quasi-uniform convergence. Furthermore, it has a structure of a Banach space if and only if (X,d) is a metric space.</Para>

Keywords: compact; Banach space; semi-Lipschitz function; normed cone; quasi-distance; complete; quasi-uniform convergence

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10474-005-0208-9

Affiliations: 1: Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, 2: Departamento de Matemáticas, Universitat Jaume I, Campus del Riu Sec 12071 Castellón, Spain,

Publication date: 2005-07-01