English
A composed map with fract is continuous under mild hypotheses: if the outer map is continuous on the product and f(s,0)=f(s,1) for all s, then the composition is continuous on a suitable domain.
Русский
Согласованное отображение с fract непрерывно на допущениях: если внешний предел непрерывен на произведении и f(s,0)=f(s,1) для всех s, то композиция непрерывна.
LaTeX
$$$$\text{ContinuousOn}(f,\text{domain}) \wedge (\forall s, f(s,0)=f(s,1)) \Rightarrow \text{Continuous}( (s,t) \mapsto f(s,\operatorname{fract}(t)) ).$$$$
Lean4
theorem tendsto_fract_right [OrderClosedTopology α] [IsTopologicalAddGroup α] (n : ℤ) :
Tendsto (fract : α → α) (𝓝[≥] n) (𝓝[≥] 0) :=
tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within _ (tendsto_fract_right' _) (Eventually.of_forall fract_nonneg)
