Mathlib Map

Theorems · Definition · general topology

TopologicalSpace.NonemptyCompacts.toCloseds

{α : Type u_1} →
  [inst : TopologicalSpace α] → [T2Space α] → TopologicalSpace.NonemptyCompacts α → TopologicalSpace.Closeds α

Reinterpret a nonempty compact as a closed set.

Defined in
Mathlib.Topology.Sets.Compacts
Cited by
15 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceT2Space
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopologicalSpace.NonemptyCompacts.isUniformEmbedding_toCloseds · cited by 2NonemptyCompacts.isUnifor…TopologicalSpace.NonemptyCompacts.isClosedEmbedding_toCloseds · cited by 1NonemptyCompacts.isClosed…TopologicalSpace.NonemptyCompacts.isClosed_in_closeds · cited by 1NonemptyCompacts.isClosed…TopologicalSpace.NonemptyCompacts.toCloseds_injective · cited by 1NonemptyCompacts.toClosed…TopologicalSpace.NonemptyCompacts.uniformContinuous_toCloseds · cited by 1NonemptyCompacts.uniformC…TopologicalSpace.NonemptyCompacts.isometry_toCloseds · cited by 1NonemptyCompacts.isometry…TopologicalSpace.NonemptyCompacts.toCloseds_prod · cited by 0NonemptyCompacts.toClosed…TopologicalSpace.NonemptyCompacts.toCloseds_singleton · cited by 0NonemptyCompacts.toClosed…TopologicalSpace.NonemptyCompacts.toCloseds_toCompacts · cited by 0NonemptyCompacts.toClosed…TopologicalSpace.NonemptyCompacts.isEmbedding_toCloseds · cited by 0NonemptyCompacts.isEmbedd…TopologicalSpace.NonemptyCompacts.mem_toCloseds · cited by 0NonemptyCompacts.mem_toCl…TopologicalSpace.NonemptyCompacts.coe_toCloseds · cited by 0NonemptyCompacts.coe_toCl…TopologicalSpace.NonemptyCompacts.continuous_toCloseds · cited by 0NonemptyCompacts.continuo…EMetric.NonemptyCompacts.isClosed_in_closeds · cited by 0NonemptyCompacts.isClosed…EMetric.NonemptyCompacts.isometry_toCloseds · cited by 0NonemptyCompacts.isometry…TopologicalSpace · cited by 24529TopologicalSpaceSetLike.coe · cited by 8199SetLike.coeT2Space · cited by 1351T2SpaceTopologicalSpace.Closeds · cited by 168TopologicalSpace.ClosedsTopologicalSpace.NonemptyCompacts · cited by 137TopologicalSpace.Nonempty…NonemptyCompacts.toClosedsCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.