Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.secondCountableTopology_iff
∀ {α : Type u_1} [inst : TopologicalSpace α],
SecondCountableTopology (TopologicalSpace.NonemptyCompacts α) ↔ SecondCountableTopology α- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites5
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
- SecondCountableTopologystatement and proof · cited by 750
- TopologicalSpace.NonemptyCompactsstatement and proof · cited by 137
- TopologicalSpace.NonemptyCompacts.isEmbedding_singletonproof · cited by 6
- Topology.IsEmbedding.secondCountableTopologyproof · cited by 6
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