Commit 2024-09-17 11:41 9a321de8
View on Github →feat(Topology/Order): Sierpiński space classifies open sets of Scott topology (#16826)
This PR shows that the Sierpiński topology coincides with the upper topology on Prop
, and hence with the Scott topology (since Prop
is a complete linear order).
This observation reveals that a subset of a preorder is open in the Scott topology if and only if its characteristic function is Scott continuous.