### Impacto

Garrido Carballo, M. Isabel and Jaramillo Aguado, Jesús Ángel
(2000)
*A Banach-Stone theorem for uniformly continuous functions.*
Monatshefte für Mathematik, 131
(3).
pp. 189-192.
ISSN 0026-9255

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## Abstract

In this note we prove that the uniformity of a complete metric space X is characterized by the vector lattice structure of the set U(X) of all uniformly continuous real functions on X.

Item Type: | Article |
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Uncontrolled Keywords: | Uniformly continuous real functions; lattice homomorphisms; Banach-Stone theorems |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15531 |

References: | Araujo J, Font JJ (2000) Linear isometries on subalgebras of uniformly continuous functions.Proc Edinburgh Math Soc 43: 139±147 Efremovich VA (1951) The geometry of proximity I. Math Sbor 31: 189±200 Engelking R (1977) General Topology. Warsaw: PWN-Polish Scienti®c Gillman L, Jerison M (1976) Rings of continuous functions. New York: Springer HernaÂndez S (1999) Uniformly continuous mappings de®ned by isometries of spaces of bounded uniformly continuous functions. Topology Atlas No 394 Hewitt E (1948) Rings of real-valued continuous functions I. Trans Amer Math Soc 64: 54±99 Isbell JR (1958) Algebras of uniformly continuous functions. Ann of Math 68: 96±125 Lacruz M, Llavona JG (1997) Composition operators between algebras of uniformly continuous functions. Arch Math 69: 52±56 Shirota T (1952) A generalization of a theorem of I. Kaplansky. Osaka Math J 4: 121±132 |

Deposited On: | 08 Jun 2012 09:24 |

Last Modified: | 06 Feb 2014 10:26 |

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