It is known that lexicographic products of paracompact LOTS's are also paracompact, see [2]. In this paper, the notion of lexicographic products of GO-spaces is defined. We characterize when a lexicographic product of GO-spaces is a LOTS. Moreover, we show that lexicographic products of paracompact GO-spaces are also paracompact. For example, we see
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the lexicographic products M×P and S×[0,1)R are LOTS's, but P×M and S×(0,1]R are not LOTS's,
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the lexicographic product Sγ of the γ-many copies of S is a LOTS iff γ is a limit ordinal,
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the lexicographic products M×P and P×M are paracompact,
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the lexicographic product Sγ is paracompact for every ordinal γ,
where P, M, S and [0,1)R denote the irrationals, the Michael line, the Sorgenfrey line and the interval [0,1) in the reals R, respectively.