Theorems · Theorem · Lie groups
mul_mem_connectedComponent_one
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : MulOneClass G] [ContinuousMul G] {g h : G},
g ∈ connectedComponent 1 → h ∈ connectedComponent 1 → g * h ∈ connectedComponent 1- 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
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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
- mul_oneproof · cited by 3,885
- MulOneClassstatement and proof · cited by 1,018
- ContinuousMulstatement and proof · cited by 343
- connectedComponentstatement and proof · cited by 68
- continuous_const_mulproof · cited by 47
- mem_connectedComponentproof · cited by 21
- connectedComponent_eqproof · cited by 6
- Continuous.image_connectedComponent_subsetproof · cited by 6
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