Theorems · Theorem · general topology
IsOpen.smul
∀ {α : Type u_2} {G : Type u_4} [inst : TopologicalSpace α] [inst_1 : Group G] [inst_2 : MulAction G α]
[ContinuousConstSMul G α] {s : Set α}, IsOpen s → ∀ (c : G), IsOpen (c • s)- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Groupstatement and proof · cited by 6,238
- IsOpenstatement and proof · cited by 2,400
- MulActionstatement and proof · cited by 1,294
- ContinuousConstSMulstatement and proof · cited by 832
- Set.smulSetstatement · cited by 608
- isOpenMap_smulproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- IsOpen.smul_leftproof · cited by 3
- MulAction.IsPretransitive.discreteTopology_iffproof · cited by 2
- IsCompact.exists_finite_cover_smulproof · cited by 1
- DenseRange.zpow_of_ergodic_mul_leftproof · cited by 1
- InfiniteGalois.fixingSubgroup_isClosedproof · cited by 0