Theorems · Theorem · Lie groups

Matrix.SpecialLinearGroup.isEmbedding_toGL

∀ {n : Type u_1} {R : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R]
  [inst_3 : TopologicalSpace R] [IsTopologicalRing R], Topology.IsEmbedding ⇑Matrix.SpecialLinearGroup.toGL

The natural map from SL n A in GL n A is an embedding, i.e. it is an injection and the topology on SL n A coincides with the subspace topology from GL n A.

Defined in

Mathlib.Topology.Algebra.Group.Matrix

Cited by

2 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingTopologicalSpaceIsTopologicalRing