On the commutativity of the powerspace constructions
General Topology
2023-06-22 v4 Logic in Computer Science
Abstract
We investigate powerspace constructions on topological spaces, with a particular focus on the category of quasi-Polish spaces. We show that the upper and lower powerspaces commute on all quasi-Polish spaces, and show more generally that this commutativity is equivalent to the topological property of consonance. We then investigate powerspace constructions on the open set lattices of quasi-Polish spaces, and provide a complete characterization of how the upper and lower powerspaces distribute over the open set lattice construction.
Cite
@article{arxiv.1709.06226,
title = {On the commutativity of the powerspace constructions},
author = {Matthew de Brecht and Tatsuji Kawai},
journal= {arXiv preprint arXiv:1709.06226},
year = {2023}
}