Theorems · Theorem · functional analysis
WithSeminorms.continuous_seminorm
∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[t : TopologicalSpace E] {p : SeminormFamily 𝕜 E ι}, WithSeminorms p → ∀ (i : ι), Continuous ⇑(p i)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 2,592
- IsTopologicalAddGroupproof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
- Seminormstatement · cited by 272
- WithSeminormsstatement and proof · cited by 69
- SeminormFamilystatement and proof · cited by 68
- continuous_normproof · cited by 36
Cited by5
Results whose statement or proof uses this declaration.
- WithSeminorms.continuous_of_isBoundedproof · cited by 4
- WithSeminorms.banach_steinhausproof · cited by 3
- WithSeminorms.toPolynormableSpaceproof · cited by 3
- WithSeminorms.continuous_iff_continuous_compproof · cited by 3
- NormedSpace.equicontinuous_TFAEproof · cited by 2