Theorems · Theorem · functional analysis
Seminorm.uniformContinuous_of_continuousAt_zero
∀ {𝕝 : Type u_6} {E : Type u_7} [inst : SeminormedRing 𝕝] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕝 E]
[inst_3 : UniformSpace E] [IsUniformAddGroup E] {p : Seminorm 𝕝 E}, ContinuousAt (⇑p) 0 → UniformContinuous ⇑p- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- UniformSpacestatement and proof · cited by 2,040
- map_zeroproof · cited by 1,614
- uniformityproof · cited by 765
- ContinuousAtstatement and proof · cited by 697
- Filter.Tendsto.compproof · cited by 560
Cited by5
Results whose statement or proof uses this declaration.
- Seminorm.continuous_of_continuousAt_zeroproof · cited by 4
- Seminorm.uniformContinuousproof · cited by 0
- Seminorm.uniformContinuous'proof · cited by 0
- Seminorm.uniformContinuous_of_forallproof · cited by 0
- Seminorm.uniformContinuous_of_forall'proof · cited by 0