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We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This answers a question of Nyikos. One of the examples is a subspace of (ω+1)×ω1. In contrast, we show that every normal subspace of a finite power of ω1 is semi-proximal.
Almontashery et al. (Wed,) studied this question.