Theorems · Theorem · general topology

tendsto_cofinite_cocompact_of_discrete

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
  [DiscreteTopology X],
  Filter.Tendsto f (Filter.cocompact X) (Filter.cocompact Y) → Filter.Tendsto f Filter.cofinite (Filter.cocompact Y)

Defined in: Mathlib.Topology.DiscreteSubset
Cited by: 1 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace DiscreteTopology

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Cites7

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

TopologicalSpacestatement and proof · cited by 24,529
Filterproof · cited by 8,121
Filter.Tendstostatement and proof · cited by 3,814
DiscreteTopologystatement and proof · cited by 373
Filter.cofinitestatement and proof · cited by 251
Filter.cocompactstatement and proof · cited by 141
Filter.cocompact_eq_cofiniteproof · cited by 7

Cited by1

Results whose statement or proof uses this declaration.

IsClosed.tendsto_coe_cofinite_of_isDiscreteproof · cited by 4