Theorems · Definition · general topology
constructibleTopologySubbasis
(X : Type u_2) → [TopologicalSpace X] → Set (Set X)
The subbasis of the constructible topology on a topological space X: It consists
of the open and compact sets of X and their complements.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsCompactproof · cited by 1,282
Cited by4
Results whose statement or proof uses this declaration.
- constructibleTopologyproof · cited by 4
- isCompact_of_mem_constructibleTopologySubbasisstatement and proof · cited by 1
- isCompact_sInter_of_subset_constructibleTopologySubbasisstatement and proof · cited by 0
- compl_mem_constructibleTopologySubbasis_iffstatement · cited by 0