symm — Mathlib

English

From a homeomorphism f preserving multiplication, mk' f h yields a ContinuousMulEquiv with the same underlying function as f.

Русский

Из гомеоморфизма f, сохраняющего умножение, mk' f h дает ContinuousMulEquiv с той же базовой функцией, что и f.

LaTeX

$$$\mathrm{mk'}(f,h)\in M\simeq_{\text{mult}} N\quad\text{and}\quad \operatorname{toFun}(\mathrm{mk'}(f,h))=f$$$

Lean4

/-- The inverse of a ContinuousMulEquiv. -/
@[to_additive (attr := symm) /-- The inverse of a ContinuousAddEquiv. -/
    ]
def symm (cme : M ≃ₜ* N) : N ≃ₜ* M :=
  { cme.toMulEquiv.symm with
    continuous_toFun := cme.continuous_invFun
    continuous_invFun := cme.continuous_toFun }

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