Theorems · Theorem · commutative algebra

MvPowerSeries.hasSubst_iff_hasEval_of_discreteTopology

∀ {σ : Type u_1} {τ : Type u_4} {S : Type u_5} [inst : CommRing S] {a : σ → MvPowerSeries τ S}
  [inst_1 : TopologicalSpace S] [DiscreteTopology S], MvPowerSeries.HasSubst a ↔ MvPowerSeries.HasEval a

A multivariate power series can be substituted if and only if it can be evaluated when the topology on the coefficients ring is the discrete topology.

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

5 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingTopologicalSpaceDiscreteTopology