diff -r c4e394a9c84c -r 402d717bb5c0 src/euclidean.rs
--- a/src/euclidean.rs	Mon Sep 01 13:51:03 2025 -0500
+++ b/src/euclidean.rs	Mon Sep 01 20:55:34 2025 -0500
@@ -4,9 +4,8 @@
 
 use crate::instance::Instance;
 use crate::linops::{VectorSpace, AXPY};
-use crate::norms::{HasDual, Reflexive};
+use crate::norms::Reflexive;
 use crate::types::*;
-use std::ops::{Add, AddAssign, Sub, SubAssign};
 
 pub mod wrap;
 
@@ -17,17 +16,13 @@
 /// The type should implement vector space operations (addition, subtraction, scalar
 /// multiplication and scalar division) along with their assignment versions, as well
 /// as an inner product.
-// TODO: remove F parameter, use AXPY::Field
+// TODO: remove F parameter, use VectorSpace::Field
 pub trait Euclidean<F: Float = f64>:
-    HasDual<F, DualSpace = Self>
-    + VectorSpace<Field = F>
-    + Reflexive<F>
-    // TODO: move the following to AXPY
-    + for<'b> Add<&'b Self, Output = <Self as VectorSpace>::Owned>
-    + for<'b> Sub<&'b Self, Output = <Self as VectorSpace>::Owned>
-    + for<'b> AddAssign<&'b Self>
-    + for<'b> SubAssign<&'b Self>
+    VectorSpace<Field = F, Owned = Self::OwnedEuclidean>
+    + Reflexive<F, DualSpace = Self::OwnedEuclidean>
 {
+    type OwnedEuclidean: ClosedEuclidean<F>;
+
     // Inner product
     fn dot<I: Instance<Self>>(&self, other: I) -> F;
 
@@ -71,10 +66,14 @@
     }
 }
 
+pub trait ClosedEuclidean<F: Float = f64>:
+    Instance<Self> + Euclidean<F, OwnedEuclidean = Self>
+{
+}
+impl<F: Float, X: Instance<X> + Euclidean<F, OwnedEuclidean = Self>> ClosedEuclidean<F> for X {}
+
 // TODO: remove F parameter, use AXPY::Field
-pub trait EuclideanMut<F: Float = f64>:
-    Euclidean<F> + AXPY<Field = F> + for<'b> AddAssign<&'b Self> + for<'b> SubAssign<&'b Self>
-{
+pub trait EuclideanMut<F: Float = f64>: Euclidean<F> + AXPY<Field = F> {
     /// In-place projection to the 2-ball.
     #[inline]
     fn proj_ball2_mut(&mut self, ρ: F) {
@@ -85,10 +84,7 @@
     }
 }
 
-impl<X, F: Float> EuclideanMut<F> for X where
-    X: Euclidean<F> + AXPY<Field = F> + for<'b> AddAssign<&'b Self> + for<'b> SubAssign<&'b Self>
-{
-}
+impl<X, F: Float> EuclideanMut<F> for X where X: Euclidean<F> + AXPY<Field = F> {}
 
 /// Trait for [`Euclidean`] spaces with dimensions known at compile time.
 pub trait StaticEuclidean<F: Float = f64>: Euclidean<F> {