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MR1600133 (99m:54020) 54F05 (54D70 54G20)
Shi, Wei-Xue A non-metrizable compact linearly ordered topological space, every subspace of which has a $\sigma$-minimal base. Proc. Amer. Math. Soc. 127 (1999), no. 9, 2783–2791.
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