Documentation

Mathlib.Topology.UniformSpace.Matrix

Uniform space structure on matrices #

instance Matrix.instUniformSpaceMatrix (m : Type u_1) (n : Type u_2) (𝕜 : Type u_3) [UniformSpace 𝕜] :
UniformSpace (Matrix m n 𝕜)
theorem Matrix.uniformity (m : Type u_1) (n : Type u_2) (𝕜 : Type u_3) [UniformSpace 𝕜] :
uniformity (Matrix m n 𝕜) = ⨅ (i : m) (j : n), Filter.comap (fun a => (Prod.fst (Matrix m n 𝕜) (Matrix m n 𝕜) a i j, Prod.snd (Matrix m n 𝕜) (Matrix m n 𝕜) a i j)) (uniformity 𝕜)
theorem Matrix.uniformContinuous (m : Type u_1) (n : Type u_2) (𝕜 : Type u_3) [UniformSpace 𝕜] {β : Type u_4} [UniformSpace β] {f : βMatrix m n 𝕜} :
UniformContinuous f ∀ (i : m) (j : n), UniformContinuous fun x => f x i j