ext_continuousMap — Mathlib

English

Given ha, any two continuous star-algebra homomorphisms from the spectrum-algebra that agree on the restriction of id are equal.

Русский

При данных ha любая пара непрерывных звёздных гомоморфизмов совпадающих на ограничении id равны между собой.

LaTeX

$$ext_continuousMap ha φ ψ hφ hψ h = φ = ψ$$

Lean4

theorem ext_continuousMap [UniqueHom R A] (a : A) [CompactSpace (spectrum R a)] (φ ψ : C(spectrum R a, R) →⋆ₐ[R] A)
    (hφ : Continuous φ) (hψ : Continuous ψ)
    (h : φ (.restrict (spectrum R a) <| .id R) = ψ (.restrict (spectrum R a) <| .id R)) : φ = ψ :=
  UniqueHom.eq_of_continuous_of_map_id (spectrum R a) φ ψ hφ hψ h

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