Theorems · Definition · measure theory

TopologicalGroup.IsSES.pullback

{A : Type u_1} →
  {B : Type u_2} →
    {C : Type u_3} →
      {E : Type u_4} →
        [inst : Group A] →
          [inst_1 : Group B] →
            [inst_2 : Group C] →
              [inst_3 : TopologicalSpace A] →
                [inst_4 : TopologicalSpace B] →
                  [inst_5 : TopologicalSpace C] →
                    {φ : A →* B} →
                      {ψ : B →* C} →
                        TopologicalGroup.IsSES φ ψ →
                          [IsTopologicalGroup A] →
                            [IsTopologicalGroup B] →
                              [inst : NormedAddCommGroup E] →
                                CompactlySupportedContinuousMap B E → B → CompactlySupportedContinuousMap A E

If φ : A →* B and ψ : B →* C define a short exact sequence of topological groups, then we can pull back a continuous compactly supported function f on B along φ to the continuous compactly supported function a ↦ f (b * φ a) on A.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Extension

Cited by

6 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupGroupTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalGroupIsTopologicalGroupNormedAddCommGroup