Fan-Gottesman type compactification of frames
Finite closed coverings of compact quantum spaces
We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...
Finite-distributive atomistic lattices