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Autor Garrido, M. Isabel |
Documentos disponibles escritos por este autor (37)
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Let X, d be a metric space. We find necessary and sufficient conditions on the space for the locally Lipschitz functions to coincide with each of two more restrictive classes of locally Lipschitz functions studied by several authors: the uniform[...]texto impreso
This paper is devoted to introduce and study two new properties of completeness in the setting of metric spaces. We will call them Bourbaki-completeness and cofinal Bourbaki-completeness. These notions came from new classes of generalized Cauchy[...]texto impreso
Recently two new types of completeness in metric spaces, called Bourbaki-completeness and cofinal Bourbaki-completeness, have been introduced in [7]. The purpose of this note is to analyze these completeness properties in the general context of [...]texto impreso
All spaces are completely regular and Hausdorff. For a space X, C(X) denotes the algebra of all bounded continuous real valued functions defined on X. In [Duke Math.J. 14, 419-427 (1947; Zbl 0029.30302)] E. Hewitt gave a uniform density theorem [...]texto impreso
Garrido, M. Isabel ; Montalvo, Francisco | Universidad de Extremadura, Departamento de Matemáticas | 1991From the introduction: "For a completely regular space X , C ? (X) denotes the algebra of all bounded real-valued continuous functions over X . We consider the topology of uniform convergence over C ? (X) . "In this paper we carry out a syste[...]texto impreso
From the text: "Problem A: Characterize (normal) spaces in which every C -embedded subset is closed. Problem B: Characterize (normal) spaces in which every C ? -embedded subset is closed. Our aim here is to call attention to the above problems,[...]texto impreso
In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions wh[...]texto impreso
Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Llavona, José G. | Elsevier Science | 2005-06-05On every real Banach space X we introduce a locally convex topology tau(p), canonically associated to the weak-polynomial topology w(P). It is proved that tau(p) is the finest locally convex topology on X which is coarser than w(P). Furthermore,[...]texto impreso
Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel | Università degli Studi di Trieste. Dipartimento di Matematica e Informatica | 2001Let L be a unital vector lattice of continuous functions on a topological space X . We study when every real lattice homomorphism on L is given by evaluation at some point of X . Some applications are given in order to obtain Banach-Stone-type[...]texto impreso
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We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manif[...]texto impreso
This note deals with some classes of bounded subsets in a metric space. Namely, sets of finite diameter, totally-bounded sets and the so-called Bourbaki-bounded sets. We will see some good and some bad properties of each class, as well as their [...]texto impreso
Let X be a set and F a family of real-valued functions (not necessarily bounded) on X. We denote by ?FX the space X endowed with the weak uniformity generated by F. and by U(?FX) the collection of uniformly continuous functions to the real line [...]texto impreso
This article provides necessary and sufficient conditions on the structure of a metric space such that for various vector lattices of real-valued Lipschitz-type functions defined on the metric space, the vector lattice is stable under pointwise [...]texto impreso
We characterize realcompact spaces for which A-realcompactness is inherited by closed subspaces