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Garrido, M. Isabel and Montalvo, Francisco
(1991)
*On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.*
Extracta Mathematicae, 6
(2-3).
pp. 156-159.
ISSN 0213-8743

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Official URL: http://www.eweb.unex.es/eweb/extracta/

## Abstract

From 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 systematic study of uniform approximation for algebras and lattices of C ∗ (X) . If F is an algebra or lattice (vector lattice, affine lattice,… ) we characterize its uniform closure and we give necessary and sufficient conditions for uniform density in C ∗ (X) . For our purposes we identify the rings C ∗ (X) and C(βX) (βX is the Stone-Čech compactification of X ). In this way, we generalize the classical results in the compact case and also obtain the generalizations by Hewitt and Blasco

Item Type: | Article |
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Subjects: | Sciences > Mathematics > Topology |

ID Code: | 21730 |

Deposited On: | 07 Jun 2013 13:50 |

Last Modified: | 19 Feb 2019 11:23 |

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