Theorems · Theorem · functional analysis
HasCompactSupport.exists_bound_of_continuous
∀ {α : Type u_1} {E : Type u_2} [inst : SeminormedAddGroup E] [inst_1 : TopologicalSpace α] {f : α → E},
HasCompactSupport f → Continuous f → ∃ C, ∀ (x : α), ‖f x‖ ≤ C- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement and proof · cited by 5,413
- Continuousstatement and proof · cited by 2,592
- SeminormedAddGroupstatement and proof · cited by 331
- HasCompactSupportstatement and proof · cited by 196
- Set.mem_rangeproof · cited by 102
- IsCompact.isBoundedproof · cited by 29
- Bornology.IsBounded.exists_norm_leproof · cited by 6
- HasCompactSupport.isCompact_rangeproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- ContDiff.lipschitzWith_of_hasCompactSupportproof · cited by 1