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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 ; 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
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
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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
For a topological space X, F(X) denotes the algebra of real-valued functions over X and C(X) the subalgebra of all functions in F(X) which are continuous. In this paper we characterize the uniformly dense linear subspaces of C(X) by means of the[...]texto impreso
Garrido, M. Isabel ; Montalvo, Francisco | Universidad de Extremadura, Departamento de Matemáticas | 1991From the introduction: "We study the uniform closure of a linear subspace of real-valued functions and we obtain, in particular, a necessary and sufficient condition for uniform density in C(X). These results generalize, for the unbounded case, [...]texto impreso
This paper deals with the equivalence between u-density and m-density for the subrings of C(X). It was proved by Kurzweil that such equivalence holds for those subrings that are closed under bounded inversion. Here an example is given in C(N) of[...]texto impreso
Garrido, M. Isabel ; Montalvo, Francisco | Universidad de Extremadura, Departamento de Matemáticas | 1994Let C(X) denote the continuous real-valued functions on a topological space X . The question of whether a u -dense subring of C(X) is m -dense is studied in this note. Recall that neighborhoods of a function f in the u -topology are determine[...]
