Theorems · Theorem · general topology
nhds_prod_le_of_disjoint_cocompact
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : Filter Y} (x : X),
Disjoint f (Filter.cocompact Y) → nhds x ×ˢ f ≤ nhdsSet ({x} ×ˢ Set.univ)- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.univstatement and proof · cited by 3,945
- Disjointstatement and proof · cited by 2,201
- SProd.sprodstatement and proof · cited by 1,750
- nhdsSetstatement and proof · cited by 267
- Filter.cocompactstatement and proof · cited by 141
- isCompact_singletonproof · cited by 32
- nhdsSet_singletonproof · cited by 19
- nhdsSet_prod_le_of_disjoint_cocompactproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_mul_nhds_zero_prod_of_disjoint_cocompactproof · cited by 2