Theorems · Theorem · general topology
Filter.Tendsto.isCompact_insert_range_of_cofinite
∀ {X : Type u} {ι : Type u_1} [inst : TopologicalSpace X] {f : ι → X} {x : X},
Filter.Tendsto f Filter.cofinite (nhds x) → IsCompact (insert x (Set.range f))- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterproof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Bot.botproof · cited by 4,720
- Set.rangestatement · cited by 4,705
- Filter.Tendstostatement and proof · cited by 3,814
- IsCompactstatement · cited by 1,282
- DiscreteTopologyproof · cited by 373
- Filter.cofinitestatement and proof · cited by 251
- continuous_of_discreteTopologyproof · cited by 20
- Filter.cocompact_eq_cofiniteproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Filter.Tendsto.isCompact_insert_rangeproof · cited by 1