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An observation on realcompact spaces

Author: Z. Ercan
Journal: Proc. Amer. Math. Soc. 134 (2006), 917-920
MSC (2000): Primary 54D60
Posted: July 19, 2005
MathSciNet review: 2180910
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Abstract: We give a characterization of realcompact spaces in terms of nets. By using the technique of this characterization we give easy proofs of the Tychonoff Theorem and the Alaoglu Theorem.

References

[1] L. Alaoglu, Weak topologies of normed linear spaces, Ann. of Math. (2) 41,(1940), 252-267. MR 0001455 (1:241e)
[2] C. D. Aliprantis and O. Burkinshaw, Positive operators, Pure and Applied Mathematics, 119. Academic Press, Inc., Orlando, FL, 1985. MR 0809372 (87h:47086)
[3] P. R. Chernoff, A simple proof of Tychonoff's theorem via nets, Amer. Math. Monthly 99 (1992), no. 10, 932-934. MR 1190558 (93m:54042)
[4] E. de Jonge and A. C. M. van Rooij, Introduction to Riesz spaces, Mathematical Centre Tracts, No. 78. Mathematisch Centrum, Amsterdam, 1977.MR 0473777 (57:13439)
[5] R. Engelking, General Topology, Heldermann Verlag Berlin, 1988.MR 1039321 (91c:54001)
[6] Z. Ercan and S. Onal, A remark on the homomorphism on , Proc. Amer. Math. Soc. (to appear).
[7] L. Gillman and M. Jerison, Rings of continuous functions, New York, 1960.MR 0116199 (22:6994)
[8] L. E. Pursell, comment: "Homomorphisms on $C(\mathbb{R} )$ ", Amer. Math. Monthly 94 (1987), no.7, 646. MR 0935848 (89b:46065)
[9] D. G. Wright, Tychonoff's theorem, Proc. Amer. Math. Soc. 120 (1994), no. 3, 985-987. MR 1170549 (94e:54032)
[10] H. J. Wu, A generalized process of Stone-Cech compactification and realcompactification of an arbitrary topological space, General topology and applications (Middletown, CT, 1988), Lecture Notes in Pure and Appl. Math., 1990(123) 269-283.MR 1057644 (91h:54039)

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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08012-3
PII: S 0002-9939(05)08012-3
Received by editor(s): September 17, 2004
Received by editor(s) in revised form: October 13, 2004
Posted: July 19, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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