Theorems · Theorem · Lie groups
stabilizer_isOpen
∀ (M : Type u_1) {X : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace X] [inst_2 : Group M]
[inst_3 : MulAction M X] [ContinuousSMul M X] [DiscreteTopology X] (x : X), IsOpen ↑(MulAction.stabilizer M x)The stabilizer of a continuous group action on a discrete space is an open subgroup.
- Defined in
- Mathlib.Topology.Algebra.MulAction
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Subgroupstatement · cited by 3,593
- IsOpenstatement · cited by 2,400
- MulActionstatement and proof · cited by 1,294
- ContinuousSMulstatement and proof · cited by 1,016
- DiscreteTopologystatement and proof · cited by 373
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- MulAction.stabilizerstatement · cited by 254
- IsOpen.preimageproof · cited by 147
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.has_decomp_quotientsproof · cited by 1
- CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroupproof · cited by 1
- CategoryTheory.PreGaloisCategory.toAut_continuousproof · cited by 1
- CategoryTheory.PreGaloisCategory.toAut_surjective_of_isPretransitiveproof · cited by 1
- CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizersproof · cited by 1
- continuousSMul_iff_stabilizer_isOpenproof · cited by 0
- Algebra.IsInvariant.exists_smul_of_under_eq_of_profiniteproof · cited by 0
- Algebra.IsInvariant.isIntegral_of_profiniteproof · cited by 0
- Ideal.Quotient.stabilizerHom_surjective_of_profiniteproof · cited by 0