Theorems · Theorem · general topology
ExtremallyDisconnected.toPreirreducibleSpace
∀ {X : Type u} [inst : TopologicalSpace X] [h : ExtremallyDisconnected X] [h' : PreconnectedSpace X],
PreirreducibleSpace XA (pre-)connected, extremally disconnected space is preirreducible.
- Defined in
- Mathlib.Topology.ExtremallyDisconnected
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.univproof · cited by 3,945
- Set.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
- closureproof · cited by 1,254
- isClosed_closureproof · cited by 195
- IsClosed.closure_eqproof · cited by 139
- PreconnectedSpacestatement and proof · cited by 64
- PreirreducibleSpacestatement · cited by 33
- dense_iff_closure_eqproof · cited by 26
- ExtremallyDisconnectedstatement and proof · cited by 23
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.