Theorems · Theorem · general topology
Function.locallyFinsuppWithin.finiteSupport
∀ {X : Type u_1} [inst : TopologicalSpace X] {U : Set X} {Y : Type u_2} [T2Space X] [inst_2 : Zero Y]
(D : Function.locallyFinsuppWithin U Y), IsCompact U → D.support.FiniteIf X is T2 and if U is compact, then the support of a function with locally finite support
within U is finite.
- Defined in
- Mathlib.Topology.LocallyFinsupp
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2SpaceZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.Finitestatement · cited by 1,814
- T2Spacestatement and proof · cited by 1,351
- IsCompactstatement and proof · cited by 1,282
- Function.locallyFinsuppWithinstatement and proof · cited by 127
- IsCompact.isClosedproof · cited by 77
- IsCompact.of_isClosed_subsetproof · cited by 67
- Function.locallyFinsuppWithin.supportstatement · cited by 29
- Function.locallyFinsuppWithin.supportWithinDomainproof · cited by 12
- IsCompact.finiteproof · cited by 5
- Function.locallyFinsuppWithin.closedSupportproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- MeromorphicOn.intervalIntegrable_log_normproof · cited by 4
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- Function.locallyFinsuppWithin.logCounting_monoproof · cited by 2
- divisor_sphere_support_finiteproof · cited by 2
- circleAverage_log_norm_factorizedRationalproof · cited by 1
- MeromorphicOn.divisor_support_finite_of_subsetproof · cited by 1
- MeromorphicOn.exists_ecanonicalDecompproof · cited by 0
- AnalyticOnNhd.sum_divisor_leproof · cited by 0