Theorems · Theorem · general topology
isCompact_of_mem_constructibleTopologySubbasis
∀ {X : Type u_1} [inst : TopologicalSpace X] [CompactSpace X] {s : Set X},
s ∈ constructibleTopologySubbasis X → IsCompact s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.ofPredproof · cited by 6,101
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- IsClosedproof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- IsClosed.isCompactproof · cited by 43
- constructibleTopologySubbasisstatement and proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isCompact_sInter_of_subset_constructibleTopologySubbasisproof · cited by 0