Theorems · Theorem · general topology
Int.tendsto_coe_cofinite
Filter.Tendsto Int.cast Filter.cofinite (Filter.cocompact ℝ)
Under the coercion from ℤ to ℝ, inverse images of compact sets are finite.
- Defined in
- Mathlib.Topology.Instances.ZMultiples
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement and proof · cited by 25,697
- SetLike.coeproof · cited by 8,199
- Filter.Tendstostatement · cited by 3,814
- AddSubgroupproof · cited by 3,232
- Filter.cofinitestatement · cited by 251
- Filter.cocompactstatement · cited by 141
- IsDiscreteproof · cited by 86
- Int.cast_injectiveproof · cited by 30
- SetLike.isDiscrete_iff_discreteTopologyproof · cited by 4
- AddMonoidHom.tendsto_coe_cofinite_of_discreteproof · cited by 2
- Int.range_castAddHomproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Real.tsum_eq_tsum_fourier_of_rpow_decayproof · cited by 2
- Real.tsum_eq_tsum_fourier_of_rpow_decay_of_summableproof · cited by 1
- ModularGroup.tendsto_lcRow0proof · cited by 1
- ModularGroup.tendsto_normSq_coprime_pairproof · cited by 1