Theorems · Theorem · functional analysis
SpectrumRestricts.compactSpace
∀ {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] {a : A} (f : C(S, R)),
SpectrumRestricts a ⇑f → ∀ [h_cpct : CompactSpace ↑(spectrum S a)], CompactSpace ↑(spectrum R a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- IsScalarTowerstatement and proof · cited by 3,896
- ContinuousMapstatement and proof · cited by 2,491
- CompactSpacestatement and proof · cited by 593
- spectrumstatement and proof · cited by 510
- Semifieldstatement and proof · cited by 439
- ContinuousMapClass.map_continuousproof · cited by 119
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