When is X × Y homeomorphic to X ×l Y?
Keywords:linearly ordered topological space, lexicographical product, homeomorphism, ordinal
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.
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
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.