Tychonoff’s Theorem as a Direct Application of Zorn’s Lemma
Pure and Applied Mathematics Journal
Volume 4, Issue 2-1, March 2015, Pages: 14-17
Received: Nov. 25, 2014;
Accepted: Dec. 11, 2014;
Published: Dec. 27, 2014
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Haruo Tsukada, Department of Information and Computer Science, Faculty of Humanity-Oriented Science and Engineering, Kindai University, 11-6 Kayanomori, Iizuka, Fukuoka, 820-8555, Japan
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A simple proof of Tychonoff’s theorem (the compactness of the product of compact spaces) as a direct application of Zorn’s lemma is given. In contrast to the classical Cartan-Bourbaki proof which uses Zorn’s lemma twice, our proof uses it only once.
Tychonoff’s Theorem, Compact Space, Product Space, Zorn’s Lemma, Axiom of Choice, Ultrafilter Theorem
To cite this article
Tychonoff’s Theorem as a Direct Application of Zorn’s Lemma, Pure and Applied Mathematics Journal. Special Issue: Abridging over Troubled Water---Scientific Foundation of Engineering Subjects.
Vol. 4, No. 2-1,
2015, pp. 14-17.
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