dual_singleton — Mathlib

English

The dual of a family of sets under a sUnion equals the infimum of duals of the sets.

Русский

Дуал объединения множества по подмножествах (sUnion) равен наименьшему дуалам подмножеств.

LaTeX

$$dual p (⋃₀ S) = sInf (dual p '' S)$$

Lean4

/-- The inner dual cone of a singleton is given by the preimage of the positive cone under the
linear map `p x`. -/
theorem dual_singleton [IsTopologicalRing R] [OrderClosedTopology R] (x : M) :
    dual p { x } = (positive R R).comap (p.toContPerfPair x) := by ext; simp

Похожие утверждения