continuous_coeff — Mathlib

English

For each d, the coefficient map coeff_d: PowerSeries(R) → R is continuous.

Русский

Для каждого фиксированного d функция коэффициента coeff_d: PowerSeries(R) → R непрерывна.

LaTeX

$$$ \\text{Continuous}( \\operatorname{coeff}_d ) $$$

Lean4

/-- Coefficients are continuous -/
theorem continuous_coeff [Semiring R] (d : ℕ) : Continuous (PowerSeries.coeff (R := R) d) :=
  continuous_pi_iff.mp continuous_id (Finsupp.single () d)

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