When is X × Y homeomorphic to X ×l Y?

Raushan Buzyakova

United States

Submitted: 2018-01-01

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Accepted: 2018-10-15

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Published: 2019-04-01

DOI: https://doi.org/10.4995/agt.2019.9135
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Keywords:

linearly ordered topological space, lexicographical product, homeomorphism, ordinal

Supporting agencies:

This research was not funded

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.

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References:

H. Bennet and D. Lutzer, Linearly ordered and generalized ordered spaces, Encyclopedia of General Topology, Elsevier, 2004. https://doi.org/10.1016/b978-044450355-8/50087-8

R. Buzyakova, Ordering a square, Topology Appl. 191 (2015), 76-81. https://doi.org/10.1016/j.topol.2015.05.020

R. Engelking, General topology, PWN, Warszawa, 1977.

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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