coe_toContinuousMapStarₐ — Mathlib

English

Compactly supported bounded continuous functions form a two-sided ideal in the ring of all bounded continuous functions: those with HasCompactSupport are closed under addition, subtraction and multiplication on both sides by arbitrary BC functions.

Русский

Функции с компактной поддержкой образуют двустороннюю идеал в кольце всех ограниченно непрерывных функций.

LaTeX

$$$$\text{compactlySupported}(\alpha, \gamma) = \{ z : \alpha \to^b \gamma \;|\; \text{HasCompactSupport}(z) \} \text{ is a two-sided ideal. }$$$$

Lean4

@[simp]
theorem coe_toContinuousMapStarₐ (f : α →ᵇ β) : (f.toContinuousMapStarₐ 𝕜 : α → β) = f :=
  rfl

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