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.
References
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" Linearly Ordered and Generalized Ordered Spaces "
- Mathematics
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 <…