TopologicallyFG.lean`

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3 declarations, 0 contain sorry, 0 declared as axioms

Topologically finitely generated algebras

The class Algebra.TopologicallyFG R S asserting that an R-algebra S is topologically generated by a finite set, together with basic consequences.

Imports (2)

Imported by 3 files

class Algebra.TopologicallyFG An R-algebra S is topologically finitely generated if there is a finite subset s ⊆ S such that the R-subalgebra generated by s is dense in S line 25 source
Source documentation
An R-algebra S is topologically finitely generated if there is a finite subset s ⊆ S such that the R-subalgebra generated by s is dense in S.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CommRing, Ring, Algebra, TopologicalSpace, IsTopologicalRing
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
class Algebra.TopologicallyFG [IsTopologicalRing S] : Prop where
…
```
instance (instance at line 28) line 28 source
lemma Algebra.TopologicallyFG.module_ext line 34 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CommRing, Ring, Algebra, TopologicalSpace, AddCommGroup, Module, T2Space, Set, Dense, Subalgebra, Algebra.adjoin, IsScalarTower, ContinuousSMul, Membership.mem, Eq, HSMul.hSMul
Proof uses: Module.ext, funext, SMul.smul, Dense.induction, Algebra.adjoin_induction, Eq.trans, RingHom, Algebra.algebraMap, algebraMap_smul, Eq.symm, HAdd.hAdd, Mathlib.Tactic.TermCongr.cHole, Module.add_smul, id, congr, congrArg, HMul.hMul, SemigroupAction.mul_smul, isClosed_eq, Continuous.comp and 12 more
59 instances, coercions and auxiliary constants left out.

Tactic trace: 8 steps
Open to load the checked before-and-after goal states.