Electronic Version 17 (1992), 181-196

E. C. Milner and Shangzhi Wang

In 1971 D.J. Lutzer [10] proved a metrization theorem for generalized order topological spaces (GO-spaces) which says that, if X is a p-embedded subspace of a linear ordered topological space, then X is metrizable if and only if it has a G_\delta-diagonal. After stating this theorem, he raised the question whether there is any larger class of GO-spaces than the p-embedded subspaces of linear ordered topological spaces for which the G_\delta-diagonal metrization theorem is true. In this paper we answer this question negatively by proving the following result. If (X, <= ,\tau) is a metrizable GO-space and d is a metric on X which is compatible with the topology \tau, then there is a metrizable linear ordered topological space (Y, <= _Y,\lambda) and a metric d^* compatible with \lambda such that (i) (X, <= ) is a subordered set of (Y, <= _Y), (ii) d^* is equivalent to d on X (equal if d is bounded), and (iii) (X,\tau) is a p-embedded closed subspace of (Y,\lambda).

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volume 17: table of contents
topology proceedings Electronic Version