Theorems · Definition · functional analysis

ContinuousLinearMap.IsInvertible

{R : Type u_1} →
  {M : Type u_2} →
    {M₂ : Type u_3} →
      [inst : TopologicalSpace M] →
        [inst_1 : TopologicalSpace M₂] →
          [inst_2 : Semiring R] →
            [inst_3 : AddCommMonoid M] →
              [inst_4 : Module R M] → [inst_5 : AddCommMonoid M₂] → [inst_6 : Module R M₂] → (M →L[R] M₂) → Prop

A continuous linear map is invertible if it is the forward direction of a continuous linear equivalence.

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

104 results in Mathlib

Foundations

Depth 21 from the axioms, rests on 184 definitions · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSemiringAddCommMonoidModuleAddCommMonoidModule