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Generation of uniformly closed algebras of functions

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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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
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
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