English

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 π\pi-tree also has a π\pi-tree. These conditions give new examples of spaces with a π\pi-tree: every at most countable power of the Sorgenfrey line and every at most countable power of the irrational Sorgenfrey line has a π ⁣\pi\!-tree. Also we show that if a space has a π\pi-tree, then its product with the Baire space, with the Sorgenfrey line, and with the countable power of the Sorgenfrey line also has a π\pi-tree.

Keywords

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}
}