HasFPowerSeriesAt — Mathlib

English

Equivalence of absolute values is equivalent to their homeomorphism relation via WithAbs.

Русский

Эквивалентность абсолютных значений эквивалентна их гомеоморфизму через WithAbs.

LaTeX

$$$ v.IsEquiv w \leftrightarrow IsHomeomorph (WithAbs.equivWithAbs v w)$$$

Lean4

/-- Given a function `f : E → F` and a formal multilinear series `p`, we say that `f` has `p` as
a power series around `x` if `f (x + y) = ∑' pₙ yⁿ` for all `y` in a neighborhood of `0`. -/
def HasFPowerSeriesAt (f : E → F) (p : FormalMultilinearSeries 𝕜 E F) (x : E) :=
  ∃ r, HasFPowerSeriesOnBall f p x r

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