Theorems · Theorem · Lie groups
vadd_connectedComponent
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [SeparatelyContinuousAdd G] (g h : G),
g +ᵥ connectedComponent h = connectedComponent (g + h)- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement · cited by 1,820
- Set.vaddSetstatement · cited by 403
- IsConnectedproof · cited by 116
- SeparatelyContinuousAddstatement and proof · cited by 83
- connectedComponentstatement · cited by 68
- Topology.IsQuotientMap.isCoinducingproof · cited by 35
- Homeomorph.isQuotientMapproof · cited by 22
- Homeomorph.addLeftproof · cited by 20
- Set.preimage_add_left_singletonproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- totallyDisconnectedSpace_iff_connectedComponent_zeroproof · cited by 0