### Impacto

Garrido Carballo, M. Isabel and Montalvo, Francisco
(2005)
*Generation of uniformly closed algebras of functions.*
Positivity, 9
(1).
pp. 81-95.
ISSN 1385-1292

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Official URL: http://www.springerlink.com/content/t558361nx4u0v441/

## Abstract

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 different methods to generate A( F) from F. For that, we introduce some families of functions which are defined in terms of suprema or sums of certain countably many functions in F. And we prove that A( F) is the uniform closure of each of these families. We obtain, in particular, a generalization of a known result about the generation of A( F) when F is a uniformly closed linear sublattice of bounded functions.

Item Type: | Article |
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Uncontrolled Keywords: | Continuous functions, lattices, algebras, inverse-closed, uniformly closed, 2-finite covers |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory Sciences > Mathematics > Topology |

ID Code: | 15516 |

References: | Anderson, F.W.: Approximation in systems of real-valued continuous functions,Trans. Amer. Math. Soc. 103 (1962), 249–271. Blasco, J.L.: On the existence of subalgebras of C(X) which are not isomorphic to C(Y) for any space Y , Acta Math. Hung. 88 (3) (2000), 221–226. Garrido, M.I. and Montalvo, F.: On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems, Acta Math. Hung. 62 (3–4) (1993), 199–208. Garrido, M.I. and Montalvo, F.: Algebraic properties of the uniform closure of spaces of continuous functions, Ann. New York Acad. Sci. 778 (1996), 101–107. Garrido, M.I. and Montalvo, F.: Countable covers and uniform approximation,Rend. Istit. Mat. Univ. Trieste 30 (1999), 91–102. Gillman, L. and Jerison, M.: Rings of Continuous Functions, Springer-Verlag, New York, 1976. Hager, A.W.: On inverse-closed subalgebras of C(X), Proc. London Math. Soc. III-19 (1969), 233–257. Hager, A.W.: An approximation technique for real-valued functions, General Top.Appl. 1 (1971), 127–133. Hager, A.W.: Real-valued functions on Alexandroff (zero-set) spaces, Comment.Math. Univ. Carolinae 16 (1975), 755–769. Hager, A.W. and Johnson, D.G.: A note of certain subaalgebras of C(X), Cand.J. Math. 20 (1968), 389–393. Henriksen, M. and Johnson, D.G.: On the structure of a class of archimedean lattice ordered algebra, Fund. Math. 50 (1961), 73–94. Mauldin, R.D.: On the Baire system generated by a linear lattice of functions, Fund.Math. 68 (1970), 51–59. Mrowka, S.: On some approximation theorems, Nieuw Archieef voor Wiskunde XVI (1968), 94–111. Mrowka, S.: Characterization of classes of functions by Lebesgue sets, Czech. Math. J. 19 (1969), 738–744. Taylor, J.C.: A class of translation lattices, Canad. J. Math. 17 (1965), 31–39. |

Deposited On: | 07 Jun 2012 08:28 |

Last Modified: | 06 Feb 2014 10:26 |

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