A regular counterexample to the 𝛾-space conjecture

Fox, Ralph; Kofner, Jacob

doi:10.1090/S0002-9939-1985-0787902-3

A regular counterexample to the $\gamma$-space conjecture
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Proc. Amer. Math. Soc. 94 (1985), 502-506 Request permission

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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