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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 [...]texto impreso
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[...]texto impreso
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.texto impreso
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[...]texto impreso
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[...]texto impreso
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 [...]texto impreso
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[...]texto impreso
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 [...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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-[...]texto impreso
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[...]texto impreso
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-[...]
