An observation on realcompact spaces

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.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-03, Vol.134 (3), p.917-920
Main Author: Ercan, Z.
Format: Article
Language:English
Subjects:
Algebra
Compactification
Continuous functions
Homomorphisms
Mathematical functions
Mathematical theorems
Topological spaces
Topological theorems
Tychonoff spaces
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Description
Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-08012-3