Theorems · Inductive type · general topology
ExtremallyDisconnected
(X : Type u) → [TopologicalSpace X] → Prop
An extremally disconnected topological space is a space in which the closure of every open set is open.
- Defined in
- Mathlib.Topology.ExtremallyDisconnected
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by46
Results whose statement or proof uses this declaration.
- Stoneanproof · cited by 19
- Stonean.toCompHausstatement and proof · cited by 5
- Condensed.StoneanCompHaus.equivalencestatement · cited by 4
- ExtremallyDisconnected.open_closurestatement and proof · cited by 4
- Profinite.liftstatement · cited by 3
- Stonean.toProfinitestatement · cited by 3
- Condensed.epi_iff_surjective_on_stoneanstatement · cited by 2
- CompactT2.ExtremallyDisconnected.projectivestatement and proof · cited by 1
- CompactT2.Projective.extremallyDisconnectedstatement · cited by 1
- extremallyDisconnected_of_homeostatement and proof · cited by 1
- Stonean.effectiveEpiFamily_tfaestatement · cited by 1
- Stonean.effectiveEpi_tfaestatement · cited by 1