11/-
2- Copyright (c) 2025 Imperial College London . All rights reserved.
2+ Copyright (c) 2025 Ruben Van de Velde and David Ledvinka . All rights reserved.
33Released under Apache 2.0 license as described in the file LICENSE.
4- Authors: Imperial College London FLT Project Contributors
4+ Authors: Ruben Van de Velde and David Ledvinka
55-/
66import Mathlib.Algebra.Group.Pi.Units
77import Mathlib.Algebra.Group.Submonoid.Units
88import Mathlib.Topology.Algebra.Constructions
99import Mathlib.Topology.Algebra.ContinuousMonoidHom
10- import Mathlib.Topology.Algebra.Group.Basic
1110
1211/-!
1312# Topological properties of units
@@ -20,12 +19,14 @@ open Units
2019
2120/-- If a submonoid is open in a topological monoid, then its units form an open subset
2221of the units of the monoid. -/
23- lemma Submonoid.units_isOpen {M : Type *} [TopologicalSpace M] [Monoid M]
22+ @[to_additive]
23+ lemma Submonoid.isOpen_units {M : Type *} [TopologicalSpace M] [Monoid M]
2424 {U : Submonoid M} (hU : IsOpen (U : Set M)) : IsOpen (U.units : Set Mˣ) :=
2525 (hU.preimage Units.continuous_val).inter (hU.preimage Units.continuous_coe_inv)
2626
2727/-- The monoid homeomorphism between the units of a product of topological monoids
2828and the product of the units of the monoids. -/
29+ @[to_additive]
2930def ContinuousMulEquiv.piUnits {ι : Type *}
3031 {M : ι → Type *} [(i : ι) → Monoid (M i)] [(i : ι) → TopologicalSpace (M i)] :
3132 (Π i, M i)ˣ ≃ₜ* Π i, (M i)ˣ where
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