Theorems · Theorem · global analysis

topologicalSemiring_of_contMDiffRing

∀ {𝕜 : Type u_1} {R : Type u_2} {E : Type u_3} {H : Type u_4} [inst : TopologicalSpace R] [inst_1 : TopologicalSpace H]
  [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E]
  [inst_5 : ChartedSpace H R] (I : ModelWithCorners 𝕜 E H) (n : WithTop ℕ∞) [inst_6 : Semiring R] [ContMDiffRing I n R],
  IsTopologicalSemiring R

A C^n (semi)ring is a topological (semi)ring. This is not an instance for technical reasons, see note [Design choices about smooth algebraic structures].

Defined in

Mathlib.Geometry.Manifold.Algebra.Structures

Cited by

0 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceNontriviallyNormedFieldNormedAddCommGroupNormedSpaceChartedSpaceSemiringContMDiffRing