Theorems · Theorem · general topology
eHolderNorm_ne_top
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {r : NNReal} {f : X → Y},
eHolderNorm r f ≠ ⊤ ↔ MemHolder r f- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- lt_top_iff_ne_topproof · cited by 95
- MemHolderstatement · cited by 26
- eHolderNormstatement and proof · cited by 16
- eHolderNorm_lt_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- eHolderNorm_eq_topproof · cited by 2
- MemHolder.eHolderNorm_ne_topproof · cited by 0