Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.regularSpace_iff
∀ {α : Type u_1} [inst : TopologicalSpace α], RegularSpace (TopologicalSpace.NonemptyCompacts α) ↔ RegularSpace α- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites6
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
- TopologicalSpace.NonemptyCompactsstatement and proof · cited by 137
- RegularSpacestatement and proof · cited by 63
- Topology.IsEmbedding.toIsInducingproof · cited by 48
- TopologicalSpace.NonemptyCompacts.isEmbedding_singletonproof · cited by 6
- Topology.IsInducing.regularSpaceproof · cited by 4
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