Theorems · Theorem · dynamical systems
IsOpen.iUnion_preimage_smul
∀ (M : Type u_1) {α : Type u_3} [inst : Monoid M] [inst_1 : TopologicalSpace α] [inst_2 : MulAction M α]
[MulAction.IsMinimal M α] {U : Set α}, IsOpen U → U.Nonempty → ⋃ c, (fun x => c • x) ⁻¹' U = Set.univ- Defined in
- Mathlib.Dynamics.Minimal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.preimagestatement · cited by 4,946
- Set.univstatement · cited by 3,945
- Monoidstatement and proof · cited by 3,887
- Set.Nonemptystatement and proof · cited by 2,627
- Set.iUnionstatement · cited by 2,483
- IsOpenstatement and proof · cited by 2,400
- MulActionstatement and proof · cited by 1,294
- Set.iUnion_eq_univ_iffproof · cited by 19
- MulAction.IsMinimalstatement and proof · cited by 16
- IsOpen.exists_smul_memproof · cited by 3
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