Theorems · Theorem · functional analysis
upperHemicontinuous_quasispectrum_nnreal
∀ (A : Type u_2) [inst : NonUnitalNormedRing A] [inst_1 : NormedSpace ℝ A] [SMulCommClass ℝ A A] [IsScalarTower ℝ A A] [CompleteSpace A], UpperHemicontinuous (quasispectrum NNReal)
The map a ↦ quasispectrum ℝ≥0 a is upper hemicontinuous.
- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Set.rangeproof · cited by 4,705
- NNRealstatement · cited by 4,310
- IsScalarTowerstatement and proof · cited by 3,896
- CompleteSpacestatement and proof · cited by 2,532
- SMulCommClassstatement and proof · cited by 1,927
- IsClosedproof · cited by 1,639
- NNReal.toRealproof · cited by 1,260
- Topology.IsEmbeddingproof · cited by 294
- quasispectrumstatement · cited by 292
- Topology.IsInducingproof · cited by 266
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSetproof · cited by 3
- continuousOn_cfcₙ_nnreal_setProd_nhdsSetproof · cited by 0