Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.isCompact_subsets_of_isCompact
∀ {α : Type u_1} [inst : TopologicalSpace α] {K : Set α}, IsCompact K → IsCompact {L | ↑L ⊆ K}- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- Set.ofPredstatement · cited by 6,101
- IsCompactstatement and proof · cited by 1,282
- TopologicalSpace.NonemptyCompactsstatement · cited by 137
- Topology.IsClosedEmbedding.isCompact_preimageproof · cited by 12
- TopologicalSpace.NonemptyCompacts.isClosedEmbedding_toCompactsproof · cited by 5
- TopologicalSpace.Compacts.isCompact_subsets_of_isCompactproof · cited by 1
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