Theorems · Theorem · Lie groups
Subgroup.isClosed_of_isOpen
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousMul G] (U : Subgroup G),
IsOpen ↑U → IsClosed ↑U- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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 and proof · cited by 2,400
- IsClosedstatement · cited by 1,639
- SeparatelyContinuousMulstatement and proof · cited by 133
- OpenSubgroup.isClosedproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.toAut_surjective_of_isPretransitiveproof · cited by 1
- Subgroup.quotient_finite_of_isOpen'proof · cited by 1