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A remark on the homomorphism on $C(X)$

Author(s): Z. Ercan; S. Onal
Journal: Proc. Amer. Math. Soc. 133 (2005), 3609-3611.
MSC (2000): Primary 46J10, 46E25
Posted: June 28, 2005
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Abstract | References | Similar articles | Additional information

Abstract: Let $X$ be a real compact space. Without using the axiom of choice we present a simple and direct proof that a non-zero homomorphism on $C(X)$ is determined by a point.

References:

[1]
R.M. Aron and G. H. Fricke, Homomorphism on $C(\mathbb{R} )$, Amer. Math. Monthly 93 (1986), no.7, 555. MR 0856297 (87i:46109)

[2]
R. Engelking, General Topology, Heldermann Verlag Berlin, 1988. MR 1039321 (91c:54001)

[3]
L. Gillman and M. Jerison, Rings of continuous functions, New York, 1960. MR 0116199 (22:6994)

[4]
L. E. Pursell, comment: ``Homomorphism on $C(\mathbb{R} )$'', Amer. Math. Monthly 94 (1987), no.7, 646. MR 0935848 (89b:46065)

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Additional Information:

Z. Ercan
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: zercan@metu.edu.tr

S. Onal
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: osul@metu.edu.tr

DOI: 10.1090/S0002-9939-05-07930-X
PII: S 0002-9939(05)07930-X
Keywords: Real compact, algebra homomorphism.
Received by editor(s): July 12, 2004
Received by editor(s) in revised form: July 30, 2004
Posted: June 28, 2005
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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