continuous_algebraMap — Mathlib

English

If E1 ≃A[R] E2 is an algebra equivalence between uniform spaces, then it is a uniform embedding provided the maps are continuous.

Русский

Если E1 ≃A[R] E2 — алгебраическое равноправие между равномерными пространствами, то оно равномерно вложено.

LaTeX

$$$IsUniformEmbedding( e )$$$

Lean4

@[continuity, fun_prop]
theorem continuous_algebraMap [ContinuousSMul R A] : Continuous (algebraMap R A) :=
  by
  rw [algebraMap_eq_smul_one']
  exact continuous_id.smul continuous_const

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