diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Field.lean b/Mathlib/Topology/Algebra/InfiniteSum/Field.lean index 5043b77bcf2075..4fd47d00a74f62 100644 --- a/Mathlib/Topology/Algebra/InfiniteSum/Field.lean +++ b/Mathlib/Topology/Algebra/InfiniteSum/Field.lean @@ -4,19 +4,21 @@ Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Analysis.Normed.Group.Continuity -import Mathlib.Analysis.Normed.Field.Basic +import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Topology.Algebra.InfiniteSum.Defs /-! # Infinite sums and products in topological fields -Lemmas on topological sums in fields (as opposed to groups). +Lemmas on topological sums in rings with a strictly multiplicative norm, of which normed fields are +the most familiar examples. -/ -section NormedField +section NormMulClass -variable {α E : Type*} [NormedField E] {f : α → E} {x : E} +variable {α E : Type*} [SeminormedCommRing E] [NormMulClass E] [NormOneClass E] + {f : α → E} {x : E} nonrec theorem HasProd.norm (hfx : HasProd f x) : HasProd (‖f ·‖) ‖x‖ := by simp only [HasProd, ← norm_prod] @@ -30,4 +32,4 @@ protected theorem Multipliable.norm_tprod (hf : Multipliable f) : ‖∏' i, f i @[deprecated (since := "2025-04-12")] alias norm_tprod := Multipliable.norm_tprod -end NormedField +end NormMulClass