Références
G. R. Allan, Embedding the algebra of formal power series in a Banach algebra,Proc. London Math. Soc.,25 (1972), 329–340.
N. L. Alling, On ordered divisible groups,Trans. Amer. Math. Soc.,94 (1960), 498–514.
N. L. Alling, On the existence of real-closed fields that are ηα-sets of power ℵα,Trans. Amer. Math. Soc.,103 (1962), 341–352.
E. Artin andO. Schreier, Algebraische Konstruktion reeller Körper,Abh. Math. Sem. Univ. Hamburg,5 (1926), 85–99.
W. Bade andP. C. Curtis, Homomorphisms of commutative Banach algebras,Amer. J. Math.,82 (1960), 589–608.
N. Bourbaki,Théorie des ensembles, Hermann (Paris, 1960).
N. Bourbaki,Algèbre, Hermann (Paris, 1960).
N. Bourbaki,Topologie générale, Hermann (Paris, 1960).
P. Erdős L. Gillman andM. Henriksen, An isomorphism theorem for real-closed fields,Ann. of Math.,6 (1955), 542–554.
J. Esterle, Semi-normes sur\(C\) (K),Proc. London Math. Soc.,38 (1978), à paraître.
L. Fuchs,Partially ordered algebraic systems, Pergamon Press (Oxford, 1963).
A. Gleyzal, Transfinite real fields,Proc. Nat. Acad. Sc.,23 (1937), 581–587.
L. Gillman, Some remarks on ηα-sets,Fund. Math.,43 (1956), 77–82.
L. Gillman, The space βN and the continuum hypothesis,Proceedings of the Second Prague Topological Symposium (1966).
L. Gillman andM. Jerison,Rings of continuous functions, Van Nostrand (New York, 1960).
K. A. Gravett, Ordered abelian groups,Quart. Journ. Math. Oxford,7 (1956), 57–63.
H. Hahn, Über die nichtarchimedischen Größensysteme,S. B. Akad. Wiss. Wien. IIa,116 (1907), 601–655.
F. Hausdorff,Grundzüge der Mengenlehre (Leipzig, 1914).
B. E. Johnson, NormingC(Ω) and related algebras,Trans. Amer. Math. Soc.,220 (1976), 37–58.
S. MacLane, The universality of power series fields,Bull. Amer. Soc.,45 (1939), 888–890.
B. H. Neumann, On ordered division rings,Trans. Amer. Math. Soc.,66 (1949), 202–252.
F. J. Rayner, Algebraically closed fields analogous to fields of Puiseux series,J. London Math. Soc., (2)8 (1974), 504–506.
F. J. Rayner, Ordered fields,Séminaire de Théorie des Nombres, Bordeaux, exposé no 1 (1975–1976).
P. Ribenboim,Théorie des groupes ordonnés. Monografias de Matematica (Bahia Blanca, 1959).
P. Ribenboim,Théorie des valuations. Presses de l'Université de Montréal (Montréal, 1964).
W. Sierpinski, Sur une propriété des ensembles ordonnés,Fund. Math.,5 (1949), 14–19.
A. M. Sinclair, Homomorphisms fromC *-algebras,Proc. London Math. Soc., (3)29 (1974), 435–452.
A. M. Sinclair, Homomorphisms fromC 0(R),J. London Math. Soc.,11 (1975), 165–174.
G. Dales, A discontinuous homomorphism from\(C\)(X),Amer. J. Math. (à paraître).
G. Dales etJ. Esterle, Discontinuous homomorphisms from\(C\)(X),Bull. Amer. Math. Soc.,83 (1977), 257–258.
J. Esterle, Sur l'existence d'un homomorphisme discontinu de\(C\)(K),Proc. London Math. Soc.,36 (1978), à paraître.
J. Esterle, Injection de semi-groupes divisibles dans des algèbres de convolution et construction d'homomorphismes discontinus de\(C\)(K),Proc. London Math. Soc.,35 (1978), à paraître.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Esterle, J. Solution d'un problème d'Erdős,Gillman etHenriksen et application a l'étude des homomorphismes de\(C\) (K)(K). Acta Mathematica Academiae Scientiarum Hungaricae 30, 113–127 (1977). https://doi.org/10.1007/BF01895655
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01895655