Theorems · Theorem · general topology
HasCompactSupport.intro
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : Zero β] {f : α → β} {K : Set α} [R1Space α],
IsCompact K → (∀ x ∉ K, f x = 0) → HasCompactSupport f- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceZeroR1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- TopologicalSpacestatement and proof · cited by 24,529
- IsCompactstatement and proof · cited by 1,282
- HasCompactSupportstatement · cited by 196
- R1Spacestatement and proof · cited by 125
- exists_compact_iff_hasCompactSupportproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.hasCompactSupportproof · cited by 4
- MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_leproof · cited by 3
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1
- ContDiffMapSupportedIn.compact_suppproof · cited by 0