Theorems · Theorem · functional analysis

ContinuousLinearMap.HasLeftInverse.isClosed_range

∀ {R : Type u_7} {E : Type u_8} {F : Type u_10} [inst : Ring R] [inst_1 : TopologicalSpace E] [inst_2 : AddCommGroup E]
  [inst_3 : Module R E] [inst_4 : TopologicalSpace F] [inst_5 : AddCommGroup F] [inst_6 : Module R F] {f : E →L[R] F}
  [T1Space F], f.HasLeftInverse → ∀ [IsTopologicalAddGroup F], IsClosed (Set.range ⇑f)

Defined in: Mathlib.Analysis.Normed.Module.ContinuousInverse
Cited by: 0 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring TopologicalSpace AddCommGroup Module TopologicalSpace AddCommGroup Module T1Space IsTopologicalAddGroup

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DFunLike.coestatement · cited by 62,936
Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
SetLike.coeproof · cited by 8,199
Ringstatement and proof · cited by 7,463
Submoduleproof · cited by 7,192
ContinuousLinearMapstatement and proof · cited by 5,352
Set.rangestatement · cited by 4,705
IsClosedstatement and proof · cited by 1,639

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