The complement of a $\sigma$-compact subset of a space with a $\pi$-tree also has a $\pi$-tree
General Topology
2016-11-22 v5
Abstract
We prove that the complement of a -compact subset of a topological space that has a -tree also has a -tree. To do this, we construct the foliage hybrid operation, which deals with foliage trees (that is, set-theoretic trees with a `leaf' at each node). Then using this operation we modify a -tree of a space and get a -tree for its subspace.
Keywords
Cite
@article{arxiv.1512.02458,
title = {The complement of a $\sigma$-compact subset of a space with a $\pi$-tree also has a $\pi$-tree},
author = {Mikhail Patrakeev},
journal= {arXiv preprint arXiv:1512.02458},
year = {2016}
}