continuousOn — Mathlib

English

If a is self-adjoint and hb : Commute a b, then for all f, Commute (cfcₙHom ha) b.

Русский

Если a самосопряжено и hb: Commute a b, то для любого f Commute (cfcₙHom ha) b.

LaTeX

$$$\forall a,b:\ IsSelfAdjoint(a) \land Commute(a,b)\Rightarrow \forall f:\ ContinuousMapZero (quasispectrum 𝕜 a).Elem 𝕜,\ Commute( cfcₙHom ha f, b).$$

Lean4

theorem continuousOn (h : ContDiffOn 𝕜 n f s) : ContinuousOn f s := fun x hx => (h x hx).continuousWithinAt

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