Theorems · Theorem · general topology
IsCompact.compl_mem_coclosedCompact_of_isClosed
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsCompact s → IsClosed s → sᶜ ∈ Filter.coclosedCompact X- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 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.
Cites9
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 · cited by 8,121
- Compl.complstatement · cited by 2,925
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- Filter.HasBasis.mem_of_memproof · cited by 63
- Filter.coclosedCompactstatement · cited by 20
- Filter.hasBasis_coclosedCompactproof · cited by 8
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.