Theorems · Theorem · dynamical systems
Dynamics.exists_isDynCoverOf_of_isCompact_invariant
∀ {X : Type u_1} {T : X → X} {U : SetRel X X} {F : Set X} [inst : UniformSpace X],
IsCompact F → Set.MapsTo T F F → U ∈ uniformity X → ∀ (n : ℕ), ∃ s, Dynamics.IsDynCoverOf T F U n ↑s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Filterstatement · cited by 8,121
- one_mulproof · cited by 2,841
- Set.iUnionproof · cited by 2,483
- Finset.cardproof · cited by 2,327
- UniformSpacestatement and proof · cited by 2,040
- IsCompactstatement and proof · cited by 1,282
- uniformitystatement and proof · cited by 765
- Set.MapsTostatement and proof · cited by 732
- SetRelstatement and proof · cited by 581
Cited by2
Results whose statement or proof uses this declaration.
- Dynamics.coverMincard_finite_of_isCompact_invariantproof · cited by 0
- Dynamics.coverEntropyEntourage_finite_of_isCompact_invariantproof · cited by 0