Theorems · Theorem · general topology
continuum_le_cardinal_of_nontriviallyNormedField
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜], Cardinal.continuum ≤ Cardinal.mk 𝕜
A complete nontrivially normed field has cardinality at least continuum.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- Norm.normproof · cited by 5,413
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- Filter.Tendstoproof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- add_zeroproof · cited by 2,707
- Cardinalstatement · cited by 2,598
- Continuousproof · cited by 2,592
- CompleteSpacestatement and proof · cited by 2,532
Cited by1
Results whose statement or proof uses this declaration.
- continuum_le_cardinal_of_moduleproof · cited by 1