Theorems · Theorem · general topology
IsCompact.nhdsSet_prod_eq_biSup
∀ {X : Type u} [inst : TopologicalSpace X] {K : Set X},
IsCompact K → ∀ {Y : Type u_2} (l : Filter Y), nhdsSet K ×ˢ l = ⨆ x ∈ K, nhds x ×ˢ l- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 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.
Cites14
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
- le_antisymmproof · cited by 2,068
- SProd.sprodstatement and proof · cited by 1,750
- le_rflproof · cited by 1,558
- IsCompactstatement and proof · cited by 1,282
- nhdsSetstatement · cited by 267
- iSup₂_leproof · cited by 96
- Filter.prod_monoproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- IsCompact.nhdsSet_prod_eqproof · cited by 5
- IsCompact.nhdsSet_inf_eq_biSupproof · cited by 3
- IsCompact.prod_nhdsSet_eq_biSupproof · cited by 3