Theorems · Theorem · general topology
isOpen_connectedComponent
∀ {α : Type u} [inst : TopologicalSpace α] [LocallyConnectedSpace α] {x : α}, IsOpen (connectedComponent x)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsOpenstatement and proof · cited by 2,400
- isOpen_univproof · cited by 112
- connectedComponentstatement · cited by 68
- LocallyConnectedSpacestatement and proof · cited by 26
- IsOpen.connectedComponentInproof · cited by 3
- connectedComponentIn_univproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- isClopen_connectedComponentproof · cited by 1
- IsLocallyConstant.of_constant_on_connected_componentsproof · cited by 1
- Pi.locallyConnectedSpace_iffproof · cited by 0