Theorems · Theorem · general topology
Filter.Tendsto.isCompact_insert_range_of_cocompact
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {y : Y},
Filter.Tendsto f (Filter.cocompact X) (nhds y) → Continuous f → IsCompact (insert y (Set.range f))- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterproof · cited by 8,121
- Set.imageproof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Filter.Tendstostatement and proof · cited by 3,814
- Compl.complproof · cited by 2,925
- Continuousstatement and proof · cited by 2,592
- Disjointproof · cited by 2,201
- Filter.univ_mem'proof · cited by 1,672
Cited by2
Results whose statement or proof uses this declaration.
- tendsto_mul_cocompact_nhds_zeroproof · cited by 1
- Filter.Tendsto.isCompact_insert_range_of_cofiniteproof · cited by 1