preimage_of_isOpen — Mathlib

English

The proof that the preorder is isomorphic to the specialization order of the upper set topology is given by explicit construction of the RelIso.

Русский

Доказательство изоморфизма предчисления: явное построение RelIso.

LaTeX

$$Proof object describing the isomorphism between α and its upper-set specialization.$$

Lean4

theorem preimage_of_isOpen (hf : IsSpectralMap f) (h₀ : IsCompact s) (h₁ : IsOpen s) : IsCompact (f ⁻¹' s) :=
  hf.isCompact_preimage_of_isOpen h₁ h₀

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