Commit 2024-09-17 11:41 9a321de8

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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.

Estimated changes

added theorem Set.Ici_False
added theorem Set.Ici_True
added theorem Set.Iic_False
added theorem Set.Iic_True
added theorem Set.Iio_False
added theorem Set.Iio_True
added theorem Set.Ioi_False
added theorem Set.Ioi_True