Theorems · Theorem · general topology
Filter.coprod_cocompact
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
(Filter.cocompact X).coprod (Filter.cocompact Y) = Filter.cocompact (X × Y)The coproduct of the cocompact filters on two topological spaces is the cocompact filter on their product.
- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 1 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- Compl.complproof · cited by 2,925
- le_antisymmproof · cited by 2,068
- SProd.sprodproof · cited by 1,750
- IsCompactproof · cited by 1,282
- sup_leproof · cited by 159
- Filter.cocompactstatement and proof · cited by 141
- continuous_fstproof · cited by 103
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_mul_cocompact_nhds_zeroproof · cited by 1