Theorems · Definition · general topology

ContinuousAffineEquiv.affineSubspaceMap

{R : Type u_1} →
  {V : Type u_2} →
    {P : Type u_3} →
      {W : Type u_4} →
        {Q : Type u_5} →
          [inst : Ring R] →
            [inst_1 : AddCommGroup V] →
              [inst_2 : Module R V] →
                [inst_3 : TopologicalSpace P] →
                  [inst_4 : AddTorsor V P] →
                    [inst_5 : AddCommGroup W] →
                      [inst_6 : Module R W] →
                        [inst_7 : TopologicalSpace Q] →
                          [inst_8 : AddTorsor W Q] →
                            (e : P ≃ᴬ[R] Q) →
                              (s : AffineSubspace R P) → [inst_9 : Nonempty ↥s] → ↥s ≃ᴬ[R] ↥(AffineSubspace.map (↑↑e) s)

A continuous affine equivalence restricts to a continuous affine equivalence between an affine subspace and its image. This is the continuous affine version of AffineEquiv.affineSubspaceMap.

Defined in

Mathlib.Topology.Algebra.AffineSubspace

Cited by

5 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleTopologicalSpaceAddTorsorAddCommGroupModuleTopologicalSpaceAddTorsorNonempty