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Theorems · Theorem · Lie groups

Subgroup.properlyDiscontinuousSMul_iff_of_isFiniteRelIndex

∀ {Γ : Type u_1} {α : Type u_2} [inst : Group Γ] [inst_1 : TopologicalSpace α] [inst_2 : MulAction Γ α]
  [ContinuousConstSMul Γ α] {G H : Subgroup Γ},
  G ≤ H → ∀ [G.IsFiniteRelIndex H], ProperlyDiscontinuousSMul (↥G) α ↔ ProperlyDiscontinuousSMul (↥H) α
Defined in
Mathlib.Topology.Algebra.Group.DiscontinuousSubgroup
Cited by
1 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupTopologicalSpaceMulActionContinuousConstSMulSubgroup.IsFiniteRelIndex
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup.Commensurable.properlyDiscontinuousSMul_iff · cited by 0Commensurable.properlyDis…TopologicalSpace · cited by 24529TopologicalSpaceGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupMulAction · cited by 1294MulActionContinuousConstSMul · cited by 832ContinuousConstSMulSubgroup.IsFiniteRelIndex · cited by 26Subgroup.IsFiniteRelIndexProperlyDiscontinuousSMul · cited by 18ProperlyDiscontinuousSMulSubgroup.properlyDiscontinuousSMul_of_le · cited by 1Subgroup.properlyDisconti…ProperlyDiscontinuousSMul.ofFiniteRelIndex · cited by 1ProperlyDiscontinuousSMul…Subgroup.properlyDiscontinuou…CITED BYCITES

Cites9

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Cited by1

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