Theorems · Theorem · general topology
TopologicalSpace.Compacts.compactSpace_iff
∀ {α : Type u_1} [inst : TopologicalSpace α], CompactSpace (TopologicalSpace.Compacts α) ↔ CompactSpace 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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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coeproof · cited by 8,199
- Set.univproof · cited by 3,945
- Set.iUnionproof · cited by 2,483
- IsCompactproof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- TopologicalSpace.Compactsstatement and proof · cited by 386
- Set.mem_singletonproof · cited by 183
- isCompact_univproof · cited by 53
- Set.biUnion_univproof · cited by 11
- TopologicalSpace.Compacts.isCompact_biUnion_coe_of_isCompactproof · cited by 2
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