continuous' — Mathlib

English

Continuity at 0 can be deduced from the prime-continuity variant.

Русский

непрерывность в нуле выводится из варианта непрерывности с апострофом.

LaTeX

$$$ \\text{continuous'}(p) \\implies \\text{continuous}(p). $$$

Lean4

protected theorem continuous' [TopologicalSpace E] [IsTopologicalAddGroup E] [ContinuousConstSMul 𝕜 E]
    {p : Seminorm 𝕜 E} {r : ℝ} (hp : p.closedBall 0 r ∈ (𝓝 0 : Filter E)) : Continuous p :=
  Seminorm.continuous_of_continuousAt_zero (continuousAt_zero' hp)

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