Theorems · Definition · functional analysis

SpectrumRestricts.homeomorph

{R : Type u_1} →
  {S : Type u_2} →
    {A : Type u_3} →
      [inst : Semifield R] →
        [inst_1 : Semifield S] →
          [inst_2 : Ring A] →
            [inst_3 : Algebra R S] →
              [inst_4 : Algebra R A] →
                [inst_5 : Algebra S A] →
                  [IsScalarTower R S A] →
                    [inst_7 : TopologicalSpace R] →
                      [inst_8 : TopologicalSpace S] →
                        [ContinuousSMul R S] →
                          {a : A} → {f : C(S, R)} → SpectrumRestricts a ⇑f → ↑(spectrum S a) ≃ₜ ↑(spectrum R a)

The homeomorphism spectrum S a ≃ₜ spectrum R a induced by SpectrumRestricts a f.

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict

Cited by

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldSemifieldRingAlgebraAlgebraAlgebraIsScalarTowerTopologicalSpaceTopologicalSpaceContinuousSMul