Theorems · Theorem · Lie groups
add_mem_connectedComponent_zero
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddZeroClass G] [ContinuousAdd G] {g h : G},
g ∈ connectedComponent 0 → h ∈ connectedComponent 0 → g + h ∈ connectedComponent 0- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 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.imageproof · cited by 5,609
- add_zeroproof · cited by 2,707
- AddZeroClassstatement and proof · cited by 1,237
- ContinuousAddstatement and proof · cited by 777
- connectedComponentstatement and proof · cited by 68
- continuous_const_addproof · cited by 23
- mem_connectedComponentproof · cited by 21
- connectedComponent_eqproof · cited by 6
- Continuous.image_connectedComponent_subsetproof · cited by 6
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.