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On the commutativity of the powerspace constructions. (English) Zbl 07093560
Summary: 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.

06D22 Frames, locales
03E15 Descriptive set theory
06B35 Continuous lattices and posets, applications
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Full Text: arXiv
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