isInducing_toGL — Mathlib

English

The map toGL is inducing, i.e., the topology on SL is the pullback of the topology from GL via toGL.

Русский

Отображение toGL индукционное; топология на SL вытягивается из GL через toGL.

LaTeX

$$Topology.IsInducing(toGL : SL(n,R) → GL(n,R))$$

Lean4

/-- 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`. -/
theorem isInducing_toGL : Topology.IsInducing (toGL : SL n R → GL n R) :=
  .of_comp continuous_toGL Units.continuous_val (Topology.IsInducing.induced _)

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