uniformContinuousConstSMul_of_continuousConstSMul

English

If a ring homomorphism f is uniform inducing, the pullback of a completable top field along f is again a completable top field.

Русский

Если кольцевой гомоморфизм f равномерно индуцирует, обратная стрелка вдоль f сохраняет структуру completableTopField.

LaTeX

$$$\text{CompletableTopField}(\alpha)$ from uniform inducing $f: \alpha \to \beta$$$

Lean4

/-- A `DistribMulAction` that is continuous on a uniform group is uniformly continuous.
This can't be an instance due to it forming a loop with
`UniformContinuousConstSMul.to_continuousConstSMul` -/
theorem uniformContinuousConstSMul_of_continuousConstSMul [Monoid R] [AddGroup M] [DistribMulAction R M]
    [UniformSpace M] [IsUniformAddGroup M] [ContinuousConstSMul R M] : UniformContinuousConstSMul R M :=
  ⟨fun r =>
    uniformContinuous_of_continuousAt_zero (DistribMulAction.toAddMonoidHom M r)
      (Continuous.continuousAt (continuous_const_smul r))⟩

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