Theorems · Theorem · functional analysis
mem_closure_zero_iff_norm
∀ {E : Type u_4} [inst : SeminormedAddGroup E] {x : E}, x ∈ closure {0} ↔ ‖x‖ = 0- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- closurestatement · cited by 1,254
- norm_nonnegproof · cited by 725
- SeminormedAddGroupstatement and proof · cited by 331
- LE.le.ge_iff_eq'proof · cited by 50
- mem_closedBall_zero_iffproof · cited by 16
- Metric.closedBall_zero'proof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Seminorm.map_eq_zero_of_norm_eq_zeroproof · cited by 1
- norm_image_of_norm_eq_zeroproof · cited by 1
- closure_zero_eqproof · cited by 0