Theorems · Theorem · functional analysis
ContinuousLinearMap.toSpanSingleton_inj
∀ {R₁ : Type u_1} [inst : Semiring R₁] {M₂ : Type u_6} [inst_1 : TopologicalSpace M₂] [inst_2 : AddCommMonoid M₂]
[inst_3 : Module R₁ M₂] [inst_4 : TopologicalSpace R₁] [inst_5 : ContinuousSMul R₁ M₂] {f f' : M₂},
ContinuousLinearMap.toSpanSingleton R₁ f = ContinuousLinearMap.toSpanSingleton R₁ f' ↔ f = f'- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousLinearMapstatement · cited by 5,352
- one_smulproof · cited by 1,374
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousLinearMap.toSpanSingletonstatement · cited by 133
Cited by2
Results whose statement or proof uses this declaration.
- UniqueDiffWithinAt.eq_derivproof · cited by 6
- HasDerivAt.uniqueproof · cited by 4