Theorems · Theorem · general topology
TopologicalSpace.isOpen_of_mem_countableBasis
∀ {α : Type u} [t : TopologicalSpace α] [inst : SecondCountableTopology α] {s : Set α},
s ∈ TopologicalSpace.countableBasis α → IsOpen s- Defined in
- Mathlib.Topology.Bases
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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
- IsOpenstatement · cited by 2,400
- SecondCountableTopologystatement and proof · cited by 750
- TopologicalSpace.IsTopologicalBasis.isOpenproof · cited by 31
- TopologicalSpace.countableBasisstatement and proof · cited by 14
- TopologicalSpace.isBasis_countableBasisproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- countable_setOfPred_covBy_rightproof · cited by 3
- countable_setOfPred_covBy_leftproof · cited by 2
- ContinuousMap.secondCountableTopologyproof · cited by 0
- MeasureTheory.Conservative.ae_frequently_mem_of_mem_nhdsproof · cited by 0