de Brecht, Matthew and Kawai, Tatsuji - On the commutativity of the powerspace constructions

lmcs:3945 - Logical Methods in Computer Science, August 8, 2019, Volume 15, Issue 3 - https://doi.org/10.23638/LMCS-15(3:13)2019
On the commutativity of the powerspace constructions

Authors: de Brecht, Matthew and Kawai, Tatsuji

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.


Volume: Volume 15, Issue 3
Published on: August 8, 2019
Submitted on: September 20, 2017
Keywords: Mathematics - General Topology,Computer Science - Logic in Computer Science


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