Theorems · Theorem · functional analysis
LinearMap.isClosed_range_coe
∀ (M₁ : Type u_1) (M₂ : Type u_2) {R : Type u_4} {S : Type u_5} [inst : TopologicalSpace M₂] [T2Space M₂]
[inst_2 : Semiring R] [inst_3 : Semiring S] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂]
[inst_6 : Module R M₁] [inst_7 : Module S M₂] [ContinuousConstSMul S M₂] [ContinuousAdd M₂] (σ : R →+* S),
IsClosed (Set.range DFunLike.coe)- Defined in
- Mathlib.Topology.Algebra.Module.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Set.rangestatement and proof · cited by 4,705
- IsClosedstatement · cited by 1,639
- T2Spacestatement and proof · cited by 1,351
- closureproof · cited by 1,254
- ContinuousConstSMulstatement and proof · cited by 832
Cited by1
Results whose statement or proof uses this declaration.
- UniformConvergenceCLM.completeSpaceproof · cited by 1