Theorems · Theorem · general topology
exists_compact_iff_hasCompactSupport
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : Zero β] {f : α → β} [R1Space α],
(∃ K, IsCompact K ∧ ∀ x ∉ K, f x = 0) ↔ HasCompactSupport f- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 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.
Cites12
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
- closureproof · cited by 1,254
- Function.supportproof · cited by 610
- HasCompactSupportstatement and proof · cited by 196
- R1Spacestatement and proof · cited by 125
- Set.mem_compl_iffproof · cited by 53
- Set.compl_subset_complproof · cited by 50
- Function.notMem_supportproof · cited by 29
- hasCompactSupport_defproof · cited by 6
- exists_isCompact_superset_iffproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- HasCompactSupport.introproof · cited by 4
- HasCompactSupport.exists_pos_le_normproof · cited by 1
- HasCompactSupport.contDiff_convolution_rightproof · cited by 1