Theorems · Theorem · general topology
uniformEquicontinuous_of_equicontinuousAt_zero
∀ {ι : Type u_1} {G : Type u_2} {M : Type u_3} {hom : Type u_4} [inst : UniformSpace G] [inst_1 : UniformSpace M]
[inst_2 : AddGroup G] [inst_3 : AddGroup M] [IsUniformAddGroup G] [IsUniformAddGroup M] [inst_6 : FunLike hom G M]
[AddMonoidHomClass hom G M] (F : ι → hom),
EquicontinuousAt (DFunLike.coe ∘ F) 0 → UniformEquicontinuous (DFunLike.coe ∘ F)- Defined in
- Mathlib.Topology.Algebra.Equicontinuity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomproof · cited by 3,230
- FunLikestatement and proof · cited by 2,560
- UniformSpacestatement and proof · cited by 2,040
- map_zeroproof · cited by 1,614
- map_addproof · cited by 964
- IsUniformAddGroupstatement and proof · cited by 342
- AddMonoidHomClassstatement and proof · cited by 252
- Function.swapproof · cited by 216
- UniformFunproof · cited by 106
- EquicontinuousAtstatement and proof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- NormedSpace.equicontinuous_TFAEproof · cited by 2
- WithSeminorms.equicontinuous_TFAEproof · cited by 2