equicontinuousWithinAt_unique — Mathlib

English

If ι is unique, equicontinuous within at x is equivalent to continuity of the unique F_i at x.

Русский

Если ι уникально, эконтинуальность внутри на x эквивалентна непрерывности единственной F_i в x.

LaTeX

$$$$ [Unique ι] \{F : ι \to X \to α\} {S : Set X} {x : X} : EquicontinuousWithinAt F S x \iff ContinuousWithinAt (F default) S x. $$$$

Lean4

theorem equicontinuousWithinAt_unique [Unique ι] {F : ι → X → α} {S : Set X} {x : X} :
    EquicontinuousWithinAt F S x ↔ ContinuousWithinAt (F default) S x :=
  equicontinuousWithinAt_finite.trans Unique.forall_iff

Похожие утверждения