Theorems · Theorem · general topology
TopologicalSpace.empty_notMem_countableBasis
∀ (α : Type u) [t : TopologicalSpace α] [inst : SecondCountableTopology α], ∅ ∉ TopologicalSpace.countableBasis α
- Defined in
- Mathlib.Topology.Bases
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SecondCountableTopologystatement and proof · cited by 750
- TopologicalSpace.countableBasisstatement · cited by 14
- TopologicalSpace.exists_countable_basisproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.nonempty_of_mem_countableBasisproof · cited by 0