Theorems · Theorem · general topology
TopologicalSpace.secondCountableTopology_iInf
∀ {α : Type u_1} {ι : Sort u_2} [Countable ι] {t : ι → TopologicalSpace α},
(∀ (i : ι), SecondCountableTopology α) → SecondCountableTopology α- Defined in
- Mathlib.Topology.Bases
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- iInfstatement · cited by 1,690
- SecondCountableTopologystatement and proof · cited by 750
- Countablestatement and proof · cited by 633
- Set.countable_iUnionproof · cited by 22
- TopologicalSpace.countable_countableBasisproof · cited by 8
- TopologicalSpace.eq_generateFrom_countableBasisproof · cited by 1
- generateFrom_iUnionproof · cited by 1
- TopologicalSpace.SecondCountableTopology.mk'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PolishSpace.iInfproof · cited by 1