Completeness of Lexicographic Products of GO-Spaces
Keywords:
compact, Dedekind complete, GO-space, lexicographic product, LOTS, completeAbstract
Variations of Dedekind completeness of lexicographic products of GO-spaces are studied. As a corollary, we see that whenever $\gamma$ is limit and all GO-spaces $X_\alpha$'s have minimal elements but have no maximal elements, connectedness of a lexicographic product $\prod_{\alpha < \gamma} X_\alpha$ implies non-connectedness of all $X_\alpha$'s.
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