Theorems · Theorem · general topology
TopologicalSpace.IsTopologicalBasis.isOpen_isPreconnected
∀ {α : Type u} [inst : TopologicalSpace α] [LocallyConnectedSpace α],
TopologicalSpace.IsTopologicalBasis {s | IsOpen s ∧ IsPreconnected s}- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredstatement · cited by 6,101
- IsOpenstatement and proof · cited by 2,400
- IsPreconnectedstatement · cited by 205
- TopologicalSpace.IsTopologicalBasisstatement · cited by 126
- IsConnectedproof · cited by 116
- LocallyConnectedSpacestatement and proof · cited by 26
- Filter.HasBasis.congrproof · cited by 7
- LocallyConnectedSpace.open_connected_basisproof · cited by 6
- TopologicalSpace.IsTopologicalBasis.of_hasBasis_nhdsproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.locallyConnectedSpace_iffproof · cited by 1
- locallyConnectedSpace_iff_isTopologicalBasis_isOpen_isPreconnectedproof · cited by 0