Theorems · Theorem · general topology
Function.locallyFinsuppWithin.supportLocallyFiniteWithinDomain
∀ {X : Type u_1} [inst : TopologicalSpace X] {U : Set X} {Y : Type u_2} [inst_1 : Zero Y]
(D : Function.locallyFinsuppWithin U Y), ∀ z ∈ U, ∃ t ∈ nhds z, (t ∩ D.support).Finite- Defined in
- Mathlib.Topology.LocallyFinsupp
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.Finitestatement · cited by 1,814
- Function.locallyFinsuppWithinstatement and proof · cited by 127
- Function.locallyFinsuppWithin.supportstatement · cited by 29
- Function.locallyFinsuppWithin.supportLocallyFiniteWithinDomain'proof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Function.locallyFinsuppWithin.eq_zero_codiscreteWithinproof · cited by 2
- Function.locallyFinsuppWithin.discreteSupportproof · cited by 1
- Function.locallyFinsuppWithin.disjoint_nhdsWithin_cofinite_of_memproof · cited by 1
- Function.locallyFinsuppWithin.closedSupportproof · cited by 1
- Function.locallyFinsuppWithin.memAddSubgroupproof · cited by 0
- Function.locallyFinsuppWithin.memAddSubmonoidproof · cited by 0