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Autor Garrido, M. Isabel |
Documentos disponibles escritos por este autor (37)
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For a completely regular space X, C(X) denotes the algebra of all real-valued and continuous functions over X. This paper deals with the problem of knowing when the uniform closure of certain subsets of C(X) has certain algebraic properties. In [...]![]()
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Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Rangel, Yenny C. | Oxford University Press | 2009-12For an infinite-dimensional Riemannian manifold M we denote by C1b(M) the space of all real bounded functions of class C(1) on M with bounded derivative. In this paper we shall see how the natural structure of normed algebra on C1b(M) characteri[...]![]()
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In this note we prove that the uniformity of a complete metric space X is characterized by the vector lattice structure of the set U(X) of all uniformly continuous real functions on X.![]()
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Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Prieto Yerro, M. Ángeles | Real Academia de Ciencias Exactas, Físicas y Naturales | 2000This short article addresses natural problems such as this one: Let M and N be two Banach manifolds such that the algebras of real-analytic functions on M and N are isomorphic as algebras. Does it follow that M and N are real-analytic isom[...]![]()
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Let hX, di be a metric space. We characterise the family of subsets of X on which each locally Lipschitz function defined on X is bounded, as well as the family of subsets on which each member of two different subfamilies consisting of uniformly[...]![]()
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The authors survey some recent results concerning the question when the equality HomA=E holds for a subalgebra A of the algebra C(E) of continuous real-valued functions on a real Banach space E. A new natural proof for this equality is given in [...]![]()
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Garrido, M. Isabel ; Montalvo, Francisco | Università degli Studi di Trieste. Dipartimento di Scienze Matematiche | 1999We present, in a unified way, several results of uniform approximation for real-valued continuous and uniformly continuous functions on a space X . We obtain all of them by applying a general method of proof that involves a certain kind of count[...]![]()
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Let X be a set and F a family of real-valued functions on X. We denote by ?FX the space X endowed with the weak uniformity given by F. In this paper we provide a method of generating the set U(?FX), of all uniformly continuous real functions on [...]![]()
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For a linear sublattice F of C( X), the set of all real continuous functions on the completely regular space X, we denote by A( F) the smallest uniformly closed and inverse-closed subalgebra of C( X) that contains F. In this paper we study diffe[...]![]()
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Garrido, M. Isabel ; Gutú, Olivia ; Jaramillo Aguado, Jesús Ángel | Pergamon-Elsevier Science | 2010In order to obtain global inversion theorems for mappings between length metric spaces, we investigate sufficient conditions for a local homeomorphism to be a covering map in this context. We also provide an estimate of the domain of invertibili[...]![]()
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In this paper we study real lattice homomorphisms on a unital vector lattice L subset of C(X), where X is a completely regular space. We stress on topological properties of its structure spaces and on its representation as point evaluations. The[...]![]()
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Garrido, M. Isabel ; Gómez Gil, Javier ; Jaramillo Aguado, Jesús Ángel | Universidad de Extremadura, Departamento de Matemáticas | 1992For an algebra A of continuous real-valued functions on a topological space X, the question of whether every algebra homomorphism is a point evaluation for a point in X is considered. A variety of results are provided, such as the following. Let[...]![]()
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Garrido, M. Isabel ; Gómez Gil, Javier ; Jaramillo Aguado, Jesús Ángel | Canadian Mathematical Society | 1994Let A be an algebra of continuous real functions on a topological space X. We study when every nonzero algebra homomorphism phi:A --> R is given by evaluation at some point of X. In the case that A is the algebra of rational functions (or real-[...]![]()
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Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Rangel, Yenny C. | Universidad de Extremadura, Departamento de Matemáticas | 2010Our aim in this note is to give an extension of the classical Myers-Nakai theorem in the context of Finsler manifolds. To achieve this, we provide a general result in this line for subalgebras of bounded Lipschitz functions on length metric spac[...]![]()
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In order to find metric spaces X for which the algebra Lip*(X) of bounded Lipschitz functions on X determines the Lipschitz structure of X, we introduce the class of small-determined spaces. We show that this class includes precompact and quasi-[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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 [...]![]()
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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[...]![]()
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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,[...]![]()
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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[...]![]()
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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,[...]![]()
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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[...]