Theorems · Theorem · functional analysis
spectrum.isOpen_resolventSet
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] (a : A), IsOpen (resolventSet 𝕜 a)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsOpenstatement · cited by 2,400
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NormedRingstatement and proof · cited by 924
- continuous_constproof · cited by 278
- IsOpen.preimageproof · cited by 147
- Continuous.fun_subproof · cited by 53
- resolventSetstatement · cited by 30
- continuous_algebraMapproof · cited by 29
- Units.isOpenproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- spectrum.isClosedproof · cited by 4
- MeasureTheory.measurable_resolventproof · cited by 2