intermediate_value_univ₂_eventually₁

English

Under the same hypotheses as hull_kernel_of_isClosed, the hull of the kernel of a closed set C recovers C.

Русский

При тех же предположениях, что и в hull_kernel_of_isClosed, оболочка оболочки(kernel(C)) восстанавливает C.

LaTeX

$$$\\mathrm{hull}(T, \\ker(C)) = C$ for closed C.$$

Lean4

theorem intermediate_value_univ₂_eventually₁ [PreconnectedSpace X] {a : X} {l : Filter X} [NeBot l] {f g : X → α}
    (hf : Continuous f) (hg : Continuous g) (ha : f a ≤ g a) (he : g ≤ᶠ[l] f) : ∃ x, f x = g x :=
  let ⟨_, h⟩ := he.exists;
  intermediate_value_univ₂ hf hg ha h

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