continuousWithinAt — Mathlib

English

For e an isomorphism, the continuity on a set is preserved under composition: ContinuousOn (e ∘ f) s ↔ ContinuousOn f s.

Русский

Пусть e — изоморфизм; непрерывность композиции на множестве сохраняется: ContinuousOn (e ∘ f) s ⇔ ContinuousOn f s.

LaTeX

$$$\text{ContinuousOn}(e \circ f, s) \iff \text{ContinuousOn}(f, s)$$$

Lean4

protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} {x : M₁} :
    ContinuousWithinAt (e : M₁ → M₂) s x :=
  e.continuous.continuousWithinAt

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