Theorems · Theorem · functional analysis
Seminorm.continuous_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 : TopologicalSpace E] [IsTopologicalAddGroup E] {p : Seminorm 𝕝 E}, ContinuousAt (⇑p) 0 → Continuous ⇑p- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 118 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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Continuousstatement · cited by 2,592
- UniformSpaceproof · cited by 2,040
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- ContinuousAtstatement and proof · cited by 697
- SeminormedRingstatement and proof · cited by 446
- IsUniformAddGroupproof · cited by 342
- Seminormstatement and proof · cited by 272
Cited by4
Results whose statement or proof uses this declaration.
- Seminorm.continuousproof · cited by 2
- Seminorm.continuous'proof · cited by 2
- Seminorm.continuous_of_forallproof · cited by 1
- Seminorm.continuous_of_forall'proof · cited by 0