Theorems · Definition · geometry

ContinuousAffineMap.contLinear

{R : Type u_1} →
  {V : Type u_2} →
    {W : Type u_3} →
      {P : 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] →
                            [inst_9 : TopologicalSpace V] →
                              [IsTopologicalAddTorsor P] →
                                [inst_11 : TopologicalSpace W] → [IsTopologicalAddTorsor Q] → (P →ᴬ[R] Q) → V →L[R] W

The linear map underlying a continuous affine map is continuous.

Defined in

Mathlib.Topology.Algebra.ContinuousAffineMap

Cited by

45 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleTopologicalSpaceAddTorsorAddCommGroupModuleTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorTopologicalSpaceIsTopologicalAddTorsor