Theorems · Theorem · Lie groups
totallyDisconnectedSpace_iff_connectedComponent_zero
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [SeparatelyContinuousAdd G],
TotallyDisconnectedSpace G ↔ connectedComponent 0 = {0}- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- AddGroupstatement and proof · cited by 4,410
- add_zeroproof · cited by 2,707
- HVAdd.hVAddproof · cited by 1,820
- TotallyDisconnectedSpacestatement and proof · cited by 295
- SeparatelyContinuousAddstatement and proof · cited by 83
- connectedComponentstatement and proof · cited by 68
- vadd_eq_addproof · cited by 39
- Set.vadd_set_singletonproof · cited by 6
- connectedComponent_eq_singletonproof · cited by 4
- totallyDisconnectedSpace_iff_connectedComponent_singletonproof · cited by 4
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