When the property of having a $\pi$-tree is preserved by products
General Topology
2016-11-29 v1
Abstract
We find sufficient conditions under which the product of spaces that have a -tree also has a -tree. These conditions give new examples of spaces with a -tree: every at most countable power of the Sorgenfrey line and every at most countable power of the irrational Sorgenfrey line has a -tree. Also we show that if a space has a -tree, then its product with the Baire space, with the Sorgenfrey line, and with the countable power of the Sorgenfrey line also has a -tree.
Cite
@article{arxiv.1611.08870,
title = {When the property of having a $\pi$-tree is preserved by products},
author = {Mikhail Patrakeev},
journal= {arXiv preprint arXiv:1611.08870},
year = {2016}
}