Mathlib Map

Theorems · Definition · general topology

Function.locallyFinsuppWithin.single

{X : Type u_1} →
  [inst : TopologicalSpace X] →
    {Y : Type u_2} → [DecidableEq X] → [inst_2 : Zero Y] → X → Y → Function.locallyFinsupp X Y

Is analogy to Finsupp.single, this definition presents the indicator function of a single point as a function with locally finite support.

Defined in
Mathlib.Topology.LocallyFinsupp
Cited by
18 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceDecidableEqZero

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Function.locallyFinsuppWithin.single_apply · cited by 8locallyFinsuppWithin.sing…Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_const · cited by 4locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.single_pos · cited by 3locallyFinsuppWithin.sing…Function.locallyFinsuppWithin.coe_single · cited by 2locallyFinsuppWithin.coe_…Function.locallyFinsuppWithin.sum_apply_smul_single_eq_self_on_univ · cited by 1locallyFinsuppWithin.sum_…Function.locallyFinsuppWithin.zero_iff_logCounting_bounded · cited by 1locallyFinsuppWithin.zero…Function.locallyFinsuppWithin.logCounting_isBigO_log_of_finite_support · cited by 1locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.logCounting_single_isBigO_log · cited by 1locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.logCounting_strictMono · cited by 1locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.one_isLittleO_logCounting_single · cited by 1locallyFinsuppWithin.one_…Function.locallyFinsuppWithin.exists_single_le_pos · cited by 1locallyFinsuppWithin.exis…Function.locallyFinsuppWithin.finite_support_of_logCounting_isBigO_log · cited by 1locallyFinsuppWithin.fini…Function.locallyFinsuppWithin.single_zero · cited by 1locallyFinsuppWithin.sing…Function.locallyFinsuppWithin.sum_apply_smul_single_eq_self · cited by 0locallyFinsuppWithin.sum_…Complex.divisor_canonicalFactor · cited by 0Complex.divisor_canonical…TopologicalSpace · cited by 24529TopologicalSpaceFunction.support · cited by 610Function.supportPi.single · cited by 518Pi.singleFunction.locallyFinsupp · cited by 43Function.locallyFinsupplocallyFinsuppWithin.singleCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.