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Theorems · Inductive type · general topology

ProperlyDiscontinuousVAdd

(Γ : Type u_4) → (T : Type u_5) → [TopologicalSpace T] → [VAdd Γ T] → Prop

Class ProperlyDiscontinuousVAdd Γ T says that the additive action (+ᵥ) : Γ → T → T is properly discontinuous, that is, for any pair of compact sets K, L in T, only finitely many γ : Γ move K to have nontrivial intersection with L.

Defined in
Mathlib.Topology.Algebra.ConstMulAction
Cited by
18 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
TopologicalSpaceVAdd

Around this declaration

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

ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_self · cited by 3ProperlyDiscontinuousVAdd…ProperlyDiscontinuousVAdd.finite_disjoint_inter_image · cited by 3ProperlyDiscontinuousVAdd…properlyDiscontinuousVAdd_iff · cited by 2properlyDiscontinuousVAdd…AddSubgroup.properlyDiscontinuousVAdd_iff · cited by 2AddSubgroup.properlyDisco…Topology.IsQuotientMap.isAddQuotientCoveringMap_of_properlyDiscontinuousVAdd · cited by 1IsQuotientMap.isAddQuotie…AddSubgroup.properlyDiscontinuousVAdd_iff_of_isFiniteRelIndex · cited by 1AddSubgroup.properlyDisco…AddSubgroup.properlyDiscontinuousVAdd_of_le · cited by 1AddSubgroup.properlyDisco…Topology.IsQuotientMap.isCoveringMapOn_of_properlyDiscontinuousVAdd · cited by 1IsQuotientMap.isCoveringM…ProperlyDiscontinuousVAdd.finite_stabilizer' · cited by 1ProperlyDiscontinuousVAdd…ProperlyDiscontinuousVAdd.ofFiniteRelIndex · cited by 1ProperlyDiscontinuousVAdd…AddSubgroup.Commensurable.properlyDiscontinuousVAdd_iff · cited by 0Commensurable.properlyDis…isCoveringMapOn_quotientMk_of_properlyDiscontinuousVAdd · cited by 0isCoveringMapOn_quotientM…properlyDiscontinuousVAdd_iff_properVAdd · cited by 0properlyDiscontinuousVAdd…isAddQuotientCoveringMap_quotientMk_of_properlyDiscontinuousVAdd · cited by 0isAddQuotientCoveringMap_…AddSubgroup.properlyDiscontinuousVAdd_of_tendsto_cofinite · cited by 0AddSubgroup.properlyDisco…TopologicalSpace · cited by 24529TopologicalSpaceVAdd · cited by 616VAddProperlyDiscontinuousVAddCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.