continuousAt_equivIco — Mathlib

English

There is an open partial homeomorphism between 𝕜 and AddCircle p with source Ioo a (a+p) and target the complement of {a}.

Русский

Существует открытое частичное гомеоморфизм между 𝕜 и AddCircle p со sources Ioo a (a+p) и targetом дополнением {a}.

LaTeX

$$$$ \text{OpenPartialHomeomorph } 𝕜 \; (AddCircle\ p) $$$$

Lean4

theorem continuousAt_equivIco (hx : x ≠ a) : ContinuousAt (equivIco p a) x :=
  by
  induction x using QuotientAddGroup.induction_on
  rw [ContinuousAt, Filter.Tendsto, QuotientAddGroup.nhds_eq, Filter.map_map]
  exact (continuousAt_toIcoMod hp.out a hx).codRestrict _

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