Theorems · Theorem · functional analysis
SpectrumRestricts.lt_nnreal_iff
∀ {A : Type u_1} [inst : Ring A] [inst_1 : Algebra ℝ A] {a : A},
SpectrumRestricts a ⇑ContinuousMap.realToNNReal →
∀ {r : NNReal}, (∀ x ∈ spectrum NNReal a, x < r) ↔ ∀ x ∈ spectrum ℝ a, x < ↑r- Defined in
- Mathlib.Analysis.Real.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- NNRealstatement and proof · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- NNReal.toRealstatement and proof · cited by 1,260
- spectrumstatement and proof · cited by 510
- SpectrumRestrictsstatement and proof · cited by 51
- ContinuousMap.realToNNRealstatement and proof · cited by 44
- SpectrumRestricts.algebraMap_imageproof · cited by 12
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