Theorems · Theorem · general topology
CompactT2.Projective.extremallyDisconnected
∀ {X : Type u} [inst : TopologicalSpace X] [CompactSpace X] [T2Space X],
CompactT2.Projective X → ExtremallyDisconnected X- Defined in
- Mathlib.Topology.ExtremallyDisconnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- Set.preimageproof · cited by 4,946
- Compl.complproof · cited by 2,925
- Continuousproof · cited by 2,592
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
- SProd.sprodproof · cited by 1,750
- IsClosedproof · cited by 1,639
- T2Spacestatement and proof · cited by 1,351
- closureproof · cited by 1,254
Cited by1
Results whose statement or proof uses this declaration.
- CompactT2.projective_iff_extremallyDisconnectedproof · cited by 0