Theorems · Definition · functional analysis

ContinuousLinearMap.restrict

{R₁ : Type u_1} →
  {R₂ : Type u_2} →
    [inst : Semiring R₁] →
      [inst_1 : Semiring R₂] →
        {σ₁₂ : R₁ →+* R₂} →
          {M₁ : Type u_4} →
            {M₂ : Type u_5} →
              [inst_2 : TopologicalSpace M₁] →
                [inst_3 : AddCommMonoid M₁] →
                  [inst_4 : Module R₁ M₁] →
                    [inst_5 : TopologicalSpace M₂] →
                      [inst_6 : AddCommMonoid M₂] →
                        [inst_7 : Module R₂ M₂] →
                          (f : M₁ →SL[σ₁₂] M₂) →
                            {p : Submodule R₁ M₁} → {q : Submodule R₂ M₂} → (∀ x ∈ p, f x ∈ q) → ↥p →SL[σ₁₂] ↥q

Restrict codomain of a continuous linear map.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Restrict

Cited by

16 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModule