Theorems · Theorem · functional analysis
exists_norm_ne_zero
∀ (E : Type u_5) [inst : SeminormedAddGroup E] [NontrivialTopology E], ∃ x, ‖x‖ ≠ 0
- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- SeminormedAddGroupstatement and proof · cited by 331
- NontrivialTopologystatement and proof · cited by 46
- nontrivialTopology_iff_exists_norm_ne_zeroproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.norm_idproof · cited by 5
- exists_norm_eqproof · cited by 4
- ContinuousLinearMap.homothety_normproof · cited by 3
- exists_dual_vector'proof · cited by 0
- SeparationQuotient.norm_normedMk_eq_oneproof · cited by 0
- NormedAddGroupHom.norm_idproof · cited by 0