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The Lindelöf Tychonoff Theorem and choice principles

Published online by Cambridge University Press:  24 October 2008

G. Schlitt
G. Schlitt
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada
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Abstract

It is an important result in frame theory that the coproduct of a family of regular Lindelöf frames is Lindelöf [3]. We show that this ‘Lindelöf Tychonoff Theorem’ or ‘LTT’ is independent of ZF and indeed lies close in logical strength to the Axiom of Countable Choice, quite unlike the case with the usual (frame) Tychonoff Theorem. Along the way we construct the regular Lindelöf coreflection and obtain a simple proof of the LTT as a corollary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 57 - 65
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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