Theorems · Theorem · general topology
ContinuousMap.norm_restrict_mono_set
∀ {E : Type u_3} [inst : SeminormedAddCommGroup E] {X : Type u_4} [inst_1 : TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X}, K ≤ L → ‖ContinuousMap.restrict (↑K) f‖ ≤ ‖ContinuousMap.restrict (↑L) f‖- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousMapstatement and proof · cited by 2,491
- norm_nonnegproof · cited by 725
- TopologicalSpace.Compactsstatement and proof · cited by 386
- Set.inclusionproof · cited by 145
- ContinuousMap.restrictstatement and proof · cited by 61
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