RT Journal Article
T1 A Banach-Stone theorem for uniformly continuous functions
A1 Garrido, M. Isabel
A1 Jaramillo Aguado, Jesús Ángel
AB 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.
PB Springer-Verlag
SN 0026-9255
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/57329
UL https://hdl.handle.net/20.500.14352/57329
LA eng
NO Araujo J, Font JJ (2000) Linear isometries on subalgebras of uniformly continuous functions.Proc Edinburgh Math Soc 43: 139±147Efremovich VA (1951) The geometry of proximity I. Math Sbor 31: 189±200Engelking R (1977) General Topology. Warsaw: PWN-Polish Scienti®cGillman L, Jerison M (1976) Rings of continuous functions. New York: SpringerHernaÂndez S (1999) Uniformly continuous mappings de®ned by isometries of spaces of bounded uniformly continuous functions. Topology Atlas No 394Hewitt E (1948) Rings of real-valued continuous functions I. Trans Amer Math Soc 64: 54±99Isbell JR (1958) Algebras of uniformly continuous functions. Ann of Math 68: 96±125Lacruz M, Llavona JG (1997) Composition operators between algebras of uniformly continuous functions. Arch Math 69: 52±56Shirota T (1952) A generalization of a theorem of I. Kaplansky. Osaka Math J 4: 121±132
DS Docta Complutense
RD 29 abr 2024