Positivity

, Volume 9, Issue 1, pp 81–95

Generation of Uniformly Closed Algebras of Functions

Article

DOI: 10.1007/s11117-003-8543-y

Cite this article as:
Garrido, M.I. & Montalvo, F. Positivity (2005) 9: 81. doi:10.1007/s11117-003-8543-y

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.

Keywords

continuous functionslatticesalgebrasinverse-closeduniformly closed2-finite covers

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Dpto. de MatemáticasUniversidad de ExtremaduraBadajozSpain