instContinuousMapUniqueHom — Mathlib

English

In the complex case there is a unique continuous map-structure extension of a continuous map from C(X,ℂ) to A that preserves the star-algebra relations; i.e., there is a unique continuous map from C(X,ℂ) to A extending the given one on NNReal or Real-embedded contexts.

Русский

В комплексном случае существует единственная непрерывная расширение отображения из C(X,ℂ) в A, сохраняющее звездо-алгебраические отношения.

LaTeX

$$There exists a unique ContinuousMap.UniqueHom ℂ A extending the given structure to map from C(X,ℂ) to A.$$

Lean4

instance instContinuousMapUniqueHom [TopologicalSpace A] [T2Space A] [Ring A] [StarRing A] [Algebra ℂ A] :
    ContinuousMap.UniqueHom ℂ A :=
  inferInstance

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