Theorems · Inductive type · general topology
TopologicalSpace.NonemptyCompacts
(α : Type u_4) → [TopologicalSpace α] → Type u_4
The type of nonempty compact sets of a topological space.
- Defined in
- Mathlib.Topology.Sets.Compacts
- Cited by
- 137 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by151
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.toCompactsstatement and proof · cited by 26
- TopologicalSpace.NonemptyCompacts.mapstatement and proof · cited by 18
- TopologicalSpace.NonemptyCompacts.toClosedsstatement and proof · cited by 15
- TopologicalSpace.NonemptyCompacts.isEmbedding_toCompactsstatement · cited by 12
- TopologicalSpace.NonemptyCompacts.continuous_toCompactsstatement · cited by 8
- TopologicalSpace.NonemptyCompacts.nonemptystatement and proof · cited by 8
- TopologicalSpace.NonemptyCompacts.isUniformEmbedding_coestatement · cited by 7
- TopologicalSpace.NonemptyCompacts.extstatement and proof · cited by 6
- TopologicalSpace.NonemptyCompacts.isEmbedding_singletonstatement · cited by 6
- TopologicalSpace.NonemptyCompacts.continuous_coestatement · cited by 5
- TopologicalSpace.NonemptyCompacts.isClosedEmbedding_toCompactsstatement · cited by 5
- TopologicalSpace.NonemptyCompacts.isOpenEmbedding_toCompactsstatement · cited by 5