continuous_expUnitary — Mathlib

English

The map a ↦ expUnitary(a) is a continuous map from the self-adjoint real subspace to the unitary group.

Русский

Карта a ↦ expUnitary(a) непрерывна от подпространства самоприводных к группе унитарных.

LaTeX

$$$$\text{continuous}(\expUnitary)$$$$

Lean4

@[fun_prop]
theorem continuous_expUnitary : Continuous (expUnitary : selfAdjoint A → unitary A) :=
  by
  simp only [continuous_induced_rng, Function.comp_def, selfAdjoint.expUnitary_coe]
  fun_prop

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