Theorems · Theorem · general topology
IsCompact.prod_nhdsSet_eq_biSup
∀ {Y : Type v} [inst : TopologicalSpace Y] {K : Set Y},
IsCompact K → ∀ {X : Type u_2} (l : Filter X), l ×ˢ nhdsSet K = ⨆ y ∈ K, l ×ˢ nhds y- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- iSupstatement and proof · cited by 2,415
- SProd.sprodstatement and proof · cited by 1,750
- IsCompactstatement and proof · cited by 1,282
- Filter.mapproof · cited by 819
- nhdsSetstatement and proof · cited by 267
- iSup_congr_Propproof · cited by 247
- Filter.prod_commproof · cited by 7
- Filter.map_iSupproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsCompact.nhdsSet_prod_eqproof · cited by 5
- IsCompact.eventually_forall_of_forall_eventuallyproof · cited by 1
- IsCompact.mem_prod_nhdsSet_of_forallproof · cited by 0