When is X × Y homeomorphic to X ×l Y?

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.

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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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Published

2019-04-01

How to Cite

[1]
R. Buzyakova, “When is X × Y homeomorphic to X ×l Y?”, Appl. Gen. Topol., vol. 20, no. 1, pp. 33–41, Apr. 2019.

Issue

Section

Regular Articles