Theorems · Theorem · general topology
TopologicalSpace.isTopologicalBasis_opens
∀ {α : Type u} [t : TopologicalSpace α], TopologicalSpace.IsTopologicalBasis {U | IsOpen U}- Defined in
- Mathlib.Topology.Bases
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 70 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.
Cites6
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.ofPredstatement and proof · cited by 6,101
- IsOpenstatement and proof · cited by 2,400
- TopologicalSpace.IsTopologicalBasisstatement · cited by 126
- TopologicalSpace.isTopologicalBasis_of_isOpen_of_nhdsproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- isOpenMap_evalproof · cited by 3
- PiNat.isTopologicalBasis_cylindersproof · cited by 1
- TopologicalSpace.NonemptyCompacts.isTopologicalBasisproof · cited by 0
- Topology.IsLawson.isTopologicalBasisproof · cited by 0
- TopologicalSpace.Compacts.isTopologicalBasisproof · cited by 0