Theorems · Theorem · functional analysis
continuous_algebraMap
∀ (R : Type u_1) (A : Type u) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [inst_3 : TopologicalSpace R] [inst_4 : TopologicalSpace A] [ContinuousSMul R A], Continuous ⇑(algebraMap R A)
- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Continuousstatement and proof · cited by 2,592
- ContinuousSMulstatement and proof · cited by 1,016
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- Continuous.fun_smulproof · cited by 44
Cited by29
Results whose statement or proof uses this declaration.
- upperHemicontinuous_spectrumproof · cited by 4
- CFC.abs_eq_cfcₙ_coe_normproof · cited by 4
- MvPowerSeries.continuous_aevalproof · cited by 4
- MvPowerSeries.comp_aevalproof · cited by 3
- MvPowerSeries.hasSum_aevalproof · cited by 3
- continuous_algebraMap_iff_smulproof · cited by 2
- NumberField.InfinitePlace.Completion.liesOver_extensionEmbeddingproof · cited by 2
- MvPowerSeries.continuous_substproof · cited by 2
- Subalgebra.frontier_spectrumproof · cited by 2
- spectrum.isOpen_resolventSetproof · cited by 2
- MvPowerSeries.aeval_uniqueproof · cited by 2
- PowerSeries.hasSum_aevalproof · cited by 1