Theorems · Theorem · Lie groups
Subgroup.isOpen_of_one_mem_interior
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousMul G] (H : Subgroup G),
1 ∈ interior ↑H → IsOpen ↑HIf a subgroup of a topological group has 1 in its interior, then it is open.
- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- IsOpenstatement · cited by 2,400
- interiorstatement and proof · cited by 714
- SeparatelyContinuousMulstatement and proof · cited by 133
- mem_interior_iff_mem_nhdsproof · cited by 82
- Subgroup.isOpen_of_mem_nhdsproof · cited by 3
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