Find out how to access previewonly content
Generation of Uniformly Closed Algebras of Functions
 M. Isabel Garrido,
 Francisco Montalvo
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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 inverseclosed 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.
 Anderson, F.W. (1962) Approximation in systems of realvalued continuous functions, Trans. Amer. Math. Soc. 103: pp. 249271
 Blasco, J.L. (2000) On the existence of subalgebras of C(X) which are not isomorphic to C(Y) for any space Y. Acta Math. Hung. 88: pp. 221226
 Garrido, M.I., Montalvo, F. (1993) On some generalizations of the KakutaniStone and StoneWeierstrass theorems. Acta Math. Hung. 62: pp. 199208
 Garrido, M.I., Montalvo, F. (1996) Algebraic properties of the uniform closure of spaces of continuous functions. Ann. New York Acad. Sci. 778: pp. 101107
 Garrido, M.I., Montalvo, F. (1999) Countable covers and uniform approximation. Rend. Istit. Mat. Univ. Trieste 30: pp. 91102
 Gillman, L., Jerison, M. (1976) Rings of Continuous Functions. SpringerVerlag, New York
 Hager, A.W. (1969) On inverseclosed subalgebras of C(X). Proc. London Math. Soc. III19: pp. 233257
 Hager, A.W. (1971) An approximation technique for realvalued functions. General Top. Appl. 1: pp. 127133
 Hager, A.W. (1975) Realvalued functions on Alexandroff (zeroset) spaces. Comment. Math. Univ. Carolinae 16: pp. 755769
 Hager, A.W., Johnson, D.G. (1968) A note of certain subaalgebras of C(X). Cand. J. Math. 20: pp. 389393
 Henriksen, M., Johnson, D.G. (1961) On the structure of a class of archimedean lattice ordered algebra. Fund. Math. 50: pp. 7394
 Mauldin, R.D. (1970) On the Baire system generated by a linear lattice of functions. Fund. Math. 68: pp. 5159
 Mrowka, S. (1968) On some approximation theorems. Nieuw Archieef voor Wiskunde XVI: pp. 94111
 Mrowka, S. (1969) Characterization of classes of functions by Lebesgue sets. Czech. Math. J. 19: pp. 738744
 Taylor, J.C. (1965) A class of translation lattices. Canad. J. Math. 17: pp. 3139
 Title
 Generation of Uniformly Closed Algebras of Functions
 Journal

Positivity
Volume 9, Issue 1 , pp 8195
 Cover Date
 20050301
 DOI
 10.1007/s111170038543y
 Print ISSN
 13851292
 Online ISSN
 15729281
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 continuous functions
 lattices
 algebras
 inverseclosed
 uniformly closed
 2finite covers
 Authors

 M. Isabel Garrido ^{(1)}
 Francisco Montalvo ^{(1)}
 Author Affiliations

 1. Dpto. de Matemáticas, Universidad de Extremadura, 06071, Badajoz, Spain