Theorems · Theorem · functional analysis
spectrum.isClosed
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] (a : A), IsClosed (spectrum 𝕜 a)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteSpacestatement and proof · cited by 2,532
- IsClosedstatement · cited by 1,639
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NormedRingstatement and proof · cited by 924
- spectrumstatement · cited by 510
- IsOpen.isClosed_complproof · cited by 50
- spectrum.isOpen_resolventSetproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- spectrum.isCompactproof · cited by 5
- Subalgebra.spectrum_sUnion_connectedComponentInproof · cited by 2
- Subalgebra.frontier_subset_frontierproof · cited by 1
- IsSelfAdjoint.map_spectrum_realproof · cited by 1