Theorems · Theorem · functional analysis
Seminorm.continuous_of_le
∀ {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 q : Seminorm 𝕝 E}, Continuous ⇑q → p ≤ q → Continuous ⇑p- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Setproof · cited by 53,352
- Realstatement and proof · 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
- IsOpenproof · cited by 2,400
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- IsOpen.mem_nhdsproof · cited by 470
- SeminormedRingstatement and proof · cited by 446
- Filter.mem_of_supersetproof · cited by 308
Cited by2
Results whose statement or proof uses this declaration.
- WithSeminorms.continuous_of_isBoundedproof · cited by 4
- Seminorm.continuous_finsetSupproof · cited by 2