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Corpus ID: 119299789

When is $X\times Y$ homeomorphic to $X\times_l Y$?

@article{Buzyakova2018WhenI,
title={When is \$X\times Y\$ homeomorphic to \$X\times\_l Y\$?},
author={Raushan Z. Buzyakova},
journal={arXiv: General Topology},
year={2018}
}

We identify a class of linearly ordered topological spaces $X$ that may satisfy the property that $X\times X$ is homeomorphic to $X\times_l X$ or can be embedded into a linearly ordered space with the stated property. We justify the conjectures by partial results.

For any linearly ordered set (X, <), let I(<) be the topology on X that has the collection of all open intervals of (X, <) as a base. The topology I(<) is the open interval topology of the order <… Expand