Theorems · Theorem · general topology
hasCompactSupport_def
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : Zero β] {f : α → β},
HasCompactSupport f ↔ IsCompact (closure (Function.support f))- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- IsCompactstatement · cited by 1,282
- closurestatement · cited by 1,254
- Function.supportstatement · cited by 610
- HasCompactSupportstatement · cited by 196
Cited by6
Results whose statement or proof uses this declaration.
- exists_compact_iff_hasCompactSupportproof · cited by 3
- HasCompactSupport.comp_isClosedEmbeddingproof · cited by 3
- ExistsContDiffBumpBase.w_compact_supportproof · cited by 2
- ExistsContDiffBumpBase.u_compact_supportproof · cited by 1
- RealRMK.measure_le_of_isCompact_of_integralproof · cited by 1
- hasCompactSupport_comp_leftproof · cited by 1