Theorems · Theorem · Lie groups
Subgroup.subgroupOf_isOpen
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] (U K : Subgroup G), IsOpen ↑K → IsOpen ↑(K.subgroupOf U)- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupTopologicalSpace
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.
- Setproof · 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 and proof · cited by 2,400
- Submonoid.toSubsemigroupproof · cited by 159
- Subgroup.subgroupOfstatement · cited by 122
- Subgroup.toSubmonoidproof · cited by 114
- Continuous.isOpen_preimageproof · cited by 51
- continuous_iff_le_inducedproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroupproof · cited by 1