Theorems · Theorem · Lie groups
smul_connectedComponent
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G] (g h : G),
g • 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.
Cites12
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
- Groupstatement and proof · cited by 6,238
- Set.smulSetstatement · cited by 608
- SeparatelyContinuousMulstatement and proof · cited by 133
- IsConnectedproof · cited by 116
- connectedComponentstatement · cited by 68
- Topology.IsQuotientMap.isCoinducingproof · cited by 35
- Homeomorph.isQuotientMapproof · cited by 22
- Homeomorph.mulLeftproof · cited by 14
- Set.preimage_mul_left_singletonproof · cited by 3
- Topology.IsCoinducing.image_connectedComponentproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- totallyDisconnectedSpace_iff_connectedComponent_oneproof · cited by 0