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Pixley-Roy and the Souslin line
Proceedings of the American Mathematical Society
Necessary and sufficient conditions are given for normality and metricity of the Pixley-Roy space over a subset of the Souslin line. The purpose of this paper is to answer a question of E. Parker: for which subsets X of a Souslin  line S is the Pixley-Roy  space PXR over X normall for which is it met riel Without loss of generality, we assume that 5 is compact, connected, and without nontrivial separable subintervals. Then: S = U aSw Ka where each Ka is a Cantor set and Ka c Kß for all a < ß. Letdoi:10.1090/s0002-9939-1979-0521886-5 fatcat:mdoivghkwbc5fgawhd4b3zro6a