Scattered and paracompact order topologies
General Topology
2020-05-20 v1
Abstract
We show that (in ZFC) every infinite set S can be equipped with 2^|S| complete metrics which generate mutually non-homeomorphic scattered order topologies on S. Furthermore, we show that (in ZFC) every uncountable set S can be equipped with 2^|S| mutually non-homeomorphic scattered and compact order topologies. (This would be unprovable in ZFC for countably infinite S.) In both enumeration theorems the cardinality 2^|S| is optimal.
Keywords
Cite
@article{arxiv.2005.09368,
title = {Scattered and paracompact order topologies},
author = {Gerald Kuba},
journal= {arXiv preprint arXiv:2005.09368},
year = {2020}
}