isClosed_ker — Mathlib

English

The codRestrict construction enjoys functorial properties with respect to composition and restriction.

Русский

Конструкция codRestrict удовлетворяет свойствам сопоставления по композиции и ограничению.

LaTeX

$$$ f.codRestrict p h \text{ behaves well under composition and restriction}$$$

Lean4

theorem isClosed_ker [T1Space M₂] [FunLike F M₁ M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂] (f : F) :
    IsClosed (ker f : Set M₁) :=
  continuous_iff_isClosed.1 (map_continuous f) _ isClosed_singleton

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