Theorems · Theorem · functional analysis
WithSeminorms.continuous_real_rng
∀ {E : Type u_6} {ι : Type u_9} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E]
{p : ι → Seminorm ℝ E}, WithSeminorms p → ∀ (f : E →ₗ[ℝ] ℝ), (∃ s C, ∀ (x : E), f x ≤ (C • s.sup p) x) → Continuous ⇑f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 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 and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- NNRealstatement and proof · cited by 4,310
- Continuousstatement · cited by 2,592
- Finset.supstatement and proof · cited by 530
- Seminormstatement and proof · cited by 272
Cited by1
Results whose statement or proof uses this declaration.
- Module.Dual.exists_continuous_extension_of_le_seminorm_realproof · cited by 0