Theorems · Theorem · general topology
hasCompactSupport_iff_eventuallyEq
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : Zero β] {f : α → β},
HasCompactSupport f ↔ f =ᶠ[Filter.coclosedCompact α] 0- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, 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
- Filter.EventuallyEqstatement · cited by 1,912
- HasCompactSupportstatement · cited by 196
- Filter.coclosedCompactstatement · cited by 20
- Filter.mem_coclosedCompact_iffproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- HasCompactSupport.mul_leftproof · cited by 2
- HasCompactSupport.mul_rightproof · cited by 2
- HasCompactSupport.integral_Iic_deriv_eqproof · cited by 1
- HasCompactSupport.comp₂_leftproof · cited by 1
- HasCompactSupport.integral_Ioi_deriv_eqproof · cited by 0
- HasCompactSupport.smul_leftproof · cited by 0
- HasCompactSupport.smul_rightproof · cited by 0