Theorems · Theorem · functional analysis
DiscreteTopology.of_forall_le_norm
∀ {E : Type u_5} [inst : SeminormedAddGroup E] {r : ℝ}, 0 < r → (∀ (x : E), x ≠ 0 → r ≤ ‖x‖) → DiscreteTopology E- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- DiscreteTopologystatement · cited by 373
- SeminormedAddGroupstatement and proof · cited by 331
- dist_eq_norm_neg_addproof · cited by 46
- neg_add_eq_zeroproof · cited by 14
- DiscreteTopology.of_forall_le_distproof · cited by 2
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