Theorems · Theorem · general topology
EMetric.NonemptyCompacts.isClosed_in_closeds
Deprecated since 2026-01-08Use TopologicalSpace.NonemptyCompacts.isClosed_in_closeds instead.
∀ {α : Type u_1} [inst : EMetricSpace α] [CompleteSpace α],
IsClosed (Set.range TopologicalSpace.NonemptyCompacts.toCloseds)Alias of TopologicalSpace.NonemptyCompacts.isClosed_in_closeds.
The range of NonemptyCompacts.toCloseds is closed in a complete space
- Defined in
- Mathlib.Topology.MetricSpace.Closeds
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpaceCompleteSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement · cited by 4,705
- CompleteSpacestatement · cited by 2,532
- IsClosedstatement · cited by 1,639
- EMetricSpacestatement · cited by 242
- TopologicalSpace.Closedsstatement · cited by 168
- TopologicalSpace.NonemptyCompactsstatement · cited by 137
- TopologicalSpace.NonemptyCompacts.toClosedsstatement · cited by 15
- TopologicalSpace.NonemptyCompacts.isClosed_in_closedsproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.