Theorems · Theorem · functional analysis
LinearPMap.closure_def
∀ {R : Type u_1} {E : Type u_2} {F : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup E] [inst_2 : AddCommGroup F]
[inst_3 : Module R E] [inst_4 : Module R F] [inst_5 : TopologicalSpace E] [inst_6 : TopologicalSpace F]
[inst_7 : ContinuousAdd E] [inst_8 : ContinuousAdd F] [inst_9 : TopologicalSpace R] [inst_10 : ContinuousSMul R E]
[inst_11 : ContinuousSMul R F] {f : E →ₗ.[R] F} (hf : f.IsClosable), f.closure = Exists.choose hf- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- LinearPMapstatement and proof · cited by 179
- Submodule.topologicalClosurestatement · cited by 50
- LinearPMap.graphstatement · cited by 39
- LinearPMap.closurestatement · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- LinearPMap.IsClosable.graph_closure_eq_closure_graphproof · cited by 6