Theorems · Theorem · general topology
TopologicalSpace.Closeds.isClosed_setOfPred_totallyBounded
∀ {α : Type u_1} [inst : UniformSpace α], IsClosed {s | TotallyBounded ↑s}- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Set.ofPredstatement · cited by 6,101
- UniformSpacestatement and proof · cited by 2,040
- IsClosedstatement · cited by 1,639
- TopologicalSpace.Closedsstatement · cited by 168
- IsClosed.preimageproof · cited by 138
- TotallyBoundedstatement · cited by 79
- UniformContinuous.continuousproof · cited by 66
- TopologicalSpace.Closeds.uniformContinuous_coeproof · cited by 5
- UniformSpace.hausdorff.isClosed_setOfPred_totallyBoundedproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.isClosedEmbedding_toClosedsproof · cited by 1
- TopologicalSpace.Closeds.isClosed_setOf_totallyBoundedproof · cited by 0