uniformSpace — Mathlib

English

Let f: α → β, u1: Set of UniformSpace α, u2: UniformSpace β, and u ∈ u1. If f is uniform Continuous from u to u2, then f is UniformContinuous from sInf u1 to u2.

Русский

Пусть f: α → β, u1 множество UniformSpace α, u2 UniformSpace β, и u ∈ u1. Если f равномерно непрерывна от u до u2, то она равномерно непрерывна от sInf u1 до u2.

LaTeX

$$UniformContinuous[u, u2] f → UniformContinuous[sInf u1, u2] f$$

Lean4

/-- Uniform space structure on `ULift α`. -/
instance uniformSpace [UniformSpace α] : UniformSpace (ULift α) :=
  UniformSpace.comap ULift.down ‹_›

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