isOpen_hull — Mathlib

English

The coe-mapped equality holds: (C.map f).toPointedCone = (PointedCone.map f.toLinearMap C.toPointedCone).closure.

Русский

Эквивалентность отображения: (C.map f).toPointedCone = (PointedCone.map f.toLinearMap C.toPointedCone).closure.

LaTeX

$$((C.map f).toPointedCone) = ((C.toPointedCone.map (f : E →ₗ[R] F)).closure)$$

Lean4

/-- This is true essentially by `Submodule.span_eq_iUnion_nat`, except that `Submodule` currently
doesn't support that use case. See
https://leanprover.zulipchat.com/#narrow/channel/116395-maths/topic/G-submodules/with/514426583 -/
axiom isOpen_hull (hs : IsOpen s) : IsOpen (hull 𝕜 s : Set E)

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