Theorems · Theorem · functional analysis
AffineMap.isOpenMap
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace E] {F : Type u_5} [inst_4 : NormedAddCommGroup F] [inst_5 : NormedSpace 𝕜 F]
[CompleteSpace F] {P : Type u_6} {Q : Type u_7} [inst_7 : MetricSpace P] [inst_8 : NormedAddTorsor E P]
[inst_9 : MetricSpace Q] [inst_10 : NormedAddTorsor F Q] (f : P →ᵃ[𝕜] Q),
Continuous ⇑f → Function.Surjective ⇑f → IsOpenMap ⇑f- Defined in
- Mathlib.Analysis.Normed.Operator.Banach
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
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
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- LinearMapproof · cited by 10,215
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Continuousstatement and proof · cited by 2,592
- CompleteSpacestatement and proof · cited by 2,532
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineMapstatement and proof · cited by 674
- IsOpenMapstatement · cited by 253
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