When is X × Y homeomorphic to X ×l Y?

Raushan Buzyakova

Abstract

We identify a class of linearly ordered topological spaces X that may satisfy the property that X × X is homeomorphic to X ×l X or can be embedded into a linearly ordered space with the stated property. We justify the conjectures by partial results.


Keywords

linearly ordered topological space; lexicographical product; homeomorphism; ordinal

Subject classification

06B30; 54F05; 06A05; 54A10.

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References

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D. Lutzer, Ordered Topological Spaces, Surveys in General Topology, edited by G. M. Reed., Academic Press, New York (1980), 247-296. https://doi.org/10.1016/B978-0-12-584960-9.50014-6

M. Katetov, Complete normality of cartesian products, Fund. Math. 36 (1948), 271-274. https://doi.org/10.4064/fm-35-1-271-274

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Universitat Politècnica de València

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