nhds — Mathlib

English

If f and g are continuous on s, then the map x ↦ (f x).coprod (g x) is continuous on s.

Русский

Если f,g непрерывны на s, то x ↦ (f x).coprod (g x) непрерывно на s.

LaTeX

$$$\text{ContinuousOn } f\; s,\; \text{ContinuousOn } g\; s\Rightarrow x \mapsto (f x).coprod (g x)\text{ ContinuousOn } s$$$

Lean4

protected theorem nhds [CompleteSpace E] (e : E ≃L[𝕜] F) : range ((↑) : (E ≃L[𝕜] F) → E →L[𝕜] F) ∈ 𝓝 (e : E →L[𝕜] F) :=
  IsOpen.mem_nhds ContinuousLinearEquiv.isOpen (by simp)

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