Theorems · Theorem · general topology
Function.locallyFinsuppWithin.exists_single_le_pos
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : DecidableEq X] {D : Function.locallyFinsupp X ℤ},
0 < D → ∃ e, Function.locallyFinsuppWithin.single e 1 ≤ DEvery positive function with locally finite supports dominates a singleton indicator.
- Defined in
- Mathlib.Topology.LocallyFinsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement and proof · cited by 3,945
- LT.lt.leproof · cited by 2,189
- eq_or_neproof · cited by 1,117
- ne_of_ltproof · cited by 203
- Function.locallyFinsuppWithinproof · cited by 127
- Function.locallyFinsuppstatement and proof · cited by 43
- Function.locallyFinsuppWithin.singlestatement · cited by 18
- Function.locallyFinsuppWithin.single_applyproof · cited by 8
- Function.locallyFinsuppWithin.ext_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Function.locallyFinsuppWithin.zero_iff_logCounting_boundedproof · cited by 1