Theorems · Theorem · Lie groups
OpenSubgroup.isOpen
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] (U : OpenSubgroup G), IsOpen ↑U- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- GroupTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 8,199
- Groupstatement and proof · cited by 6,238
- IsOpenstatement · cited by 2,400
- OpenSubgroupstatement and proof · cited by 47
- OpenSubgroup.isOpen'proof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- OpenSubgroup.isClosedproof · cited by 4
- OpenSubgroup.mem_nhds_oneproof · cited by 2
- CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroupproof · cited by 1
- ProfiniteGrp.closedSubgroup_eq_sInf_openproof · cited by 0
- Subgroup.isOpen_of_openSubgroupproof · cited by 0
- NonarchimedeanGroup.nonarchimedean_of_embproof · cited by 0
- OpenSubgroup.isClopenproof · cited by 0