continuousSMul_int — Mathlib

English

If every topology ts'(i) on G has ContinuousInv, then the infimum topology has ContinuousInv.

Русский

Если каждая топология ts'(i) на G имеет ContinuousInv, то инфимум этих топологий тоже имеет ContinuousInv.

LaTeX

$$$(\forall i, \text{ContinuousInv } G) \Rightarrow \text{ContinuousInv } G\text{ in } \bigwedge_i ts'(i).$$$

Lean4

instance continuousSMul_int {A} [AddGroup A] [TopologicalSpace A] [IsTopologicalAddGroup A] : ContinuousSMul ℤ A :=
  ⟨continuous_prod_of_discrete_left.mpr continuous_zsmul⟩

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