zpow — Mathlib

English

If ts are topologies on G and ContinuousInv holds for each, then the infimum topology has ContinuousInv.

Русский

Если для каждой топологии ts на G выполнено ContinuousInv, то инфимум этих топологий имеет ContinuousInv.

LaTeX

$$$(\forall t \in ts, \text{ContinuousInv}(G)\text{ under } t) \Rightarrow \text{ContinuousInv}(G)\text{ under } sInf(ts).$$$

Lean4

@[to_additive (attr := continuity, fun_prop)]
theorem zpow {f : α → G} (h : Continuous f) (z : ℤ) : Continuous fun b => f b ^ z :=
  (continuous_zpow z).comp h

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