When is X × Y homeomorphic to X ×l Y?
Submitted: 2018-01-01
|Accepted: 2018-10-15
|Published: 2019-04-01
Downloads
Keywords:
linearly ordered topological space, lexicographical product, homeomorphism, ordinal
Supporting agencies:
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.
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