Theorems · Theorem · functional analysis

LinearPMap.IsClosable.existsUnique

∀ {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}, f.IsClosable → ∃! f', f.graph.topologicalClosure = f'.graph

The closure is unique.

Defined in: Mathlib.Topology.Algebra.Module.LinearPMap
Cited by: 0 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup AddCommGroup Module Module TopologicalSpace TopologicalSpace ContinuousAdd ContinuousAdd TopologicalSpace ContinuousSMul ContinuousSMul

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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 and proof · cited by 7,192
ContinuousSMulstatement and proof · cited by 1,016
ContinuousAddstatement and proof · cited by 777
ExistsUniquestatement · cited by 268
LinearPMapstatement and proof · cited by 179
Submodule.topologicalClosurestatement and proof · cited by 50
LinearPMap.graphstatement and proof · cited by 39

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