Theorems · Theorem · Lie groups

Matrix.SpecialLinearGroup.isInducing_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.IsInducing ⇑Matrix.SpecialLinearGroup.toGL

The natural map from SL n A to GL n A is inducing, i.e. the topology on SL n A is the pullback of the topology from GL n A.

Defined in

Mathlib.Topology.Algebra.Group.Matrix

Cited by

2 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingTopologicalSpaceIsTopologicalRing