Module

ConnectedComponentsSeparation.lean

Nyll.SchemeTheory.Topology.ConnectedComponentsSeparation
1 declaration indexed from sourceView source ↗

Hausdorff connected-component spaces

The connected-component quotient of a compact quasi-separated prespectral space is Hausdorff, even when the original space is not Hausdorff.

Declarations

SchemeTheory.t2Space_connectedComponents_of_prespectral

Clopen neighbourhoods separate distinct connected components of a compact quasi-separated prespectral space.

Source context 4 commands

Surrounding namespaces, section variables, and local commands at this declaration.

@[expose] public section
universe u
open Set TopologicalSpace
namespace SchemeTheory
theorem t2Space_connectedComponents_of_prespectral {X : Type u} [TopologicalSpace X]
    [CompactSpace X] [PrespectralSpace X] [QuasiSeparatedSpace X] :
    T2Space (ConnectedComponents X)