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A Note on the Normal Moore Space Conjecture

Published online by Cambridge University Press:  20 November 2018

Keith J. Devlin  and
Saharon Shelah
Keith J. Devlin
Affiliation:
University of Lancaster, Lancaster, England;
Saharon Shelah
Affiliation:
The Hebrew University, Jerusalem, Israel
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F. B. Jones (1937) conjectured that every normal Moore space is metrizable. He also denned a particular kind of topological space (now known as Jones' spaces), proved that they were all non-metrizable Moore spaces, but was unable to decide whether or not Jones’ spaces are normal. J. H. Silver (1967) proved that a positive solution to Jones’ conjecture was not possible, and W. Fleissner (1973) obtained an alternative proof by showing that it is not possible to prove the non-normality of Jones’ spaces. These results left open the possibility of resolving the questions from the GCH. In this paper we show that if CH be assumed, then Jones’ spaces are not normal (Devlin, Shelah, independently) and that the GCH does not lead to a positive solution to the Jones conjecture (Shelah). A brief survey of the progress on the problem to date is also included.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 241 - 251
Copyright
Copyright © Canadian Mathematical Society 1979

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