When is X × Y homeomorphic to X ×l Y?

Raushan Buzyakova

doi:10.4995/agt.2019.9135

Authors

Raushan Buzyakova

DOI:

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

Keywords:

linearly ordered topological space, lexicographical product, homeomorphism, ordinal

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.

Downloads

Download data is not yet available.

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