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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A regular counterexample to the $ \gamma$-space conjecture


Authors: Ralph Fox and Jacob Kofner
Journal: Proc. Amer. Math. Soc. 94 (1985), 502-506
MSC: Primary 54E15; Secondary 54D15, 54E30, 54G20
MathSciNet review: 787902
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Abstract: This paper presents a completely regular counterexample to the conjecture that every $ \gamma $-space is quasi-metrizable. Junnila has shown that developable $ \gamma $-spaces are quasi-metrizable; this example shows that "developable" cannot be replaced by "quasi-developable". In the process we provide a method for constructing non-$ n$-pretransitive spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0787902-3
PII: S 0002-9939(1985)0787902-3
Keywords: Quasi-metric, $ \gamma $-space, $ n$-pretransitive space, normal neighbournet, quasi-devel opable, scattered space
Article copyright: © Copyright 1985 American Mathematical Society