Theorems · Theorem · dynamical systems
Dynamics.ball_dynEntourage_mem_nhds
∀ {X : Type u_1} {T : X → X} {U : SetRel X X} [inst : UniformSpace X],
Continuous T → U ∈ uniformity X → ∀ (n : ℕ) (x : X), UniformSpace.ball x (Dynamics.dynEntourage T U n) ∈ nhds x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 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.
Cites21
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Continuousstatement and proof · cited by 2,592
- UniformSpacestatement and proof · cited by 2,040
- Set.Icoproof · cited by 799
- uniformitystatement and proof · cited by 765
- Nat.iterateproof · cited by 740
- SetRelstatement and proof · cited by 581
- Continuous.continuousAtproof · cited by 297
- UniformSpace.ballstatement and proof · cited by 113
Cited by1
Results whose statement or proof uses this declaration.
- Dynamics.IsDynCoverOf.closureproof · cited by 1