Theorems · Theorem · general topology
isConnected_univ
∀ {α : Type u} [inst : TopologicalSpace α] [ConnectedSpace α], IsConnected Set.univ- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- IsConnectedstatement · cited by 116
- ConnectedSpacestatement and proof · cited by 37
- PreconnectedSpace.isPreconnected_univproof · cited by 26
- Set.univ_nonemptyproof · cited by 21
Cited by9
Results whose statement or proof uses this declaration.
- Orientation.oangle_sign_smul_add_rightproof · cited by 6
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2
- AffineSubspace.isConnected_setOfPred_wOppSideproof · cited by 2
- AffineSubspace.isConnected_setOfPred_wSameSideproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isConnected_preimage_singletonproof · cited by 1
- Meromorphic.exists_meromorphicOrderAt_ne_top_iff_forallproof · cited by 1
- AlgebraicGeometry.GeometricallyConnected.connectedSpaceproof · cited by 1
- AnalyticOnNhd.preimage_zero_mem_codiscreteproof · cited by 1
- isConnected_setOfPred_sameRayproof · cited by 1