Theorems · Theorem · general topology
UniformContinuous.nonemptyCompacts_map
∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β}
(hf : UniformContinuous f), UniformContinuous (TopologicalSpace.NonemptyCompacts.map f ⋯)- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- UniformContinuousstatement and proof · cited by 410
- TopologicalSpace.NonemptyCompactsstatement · cited by 137
- UniformContinuous.continuousstatement · cited by 66
- UniformContinuous.compproof · cited by 60
- IsUniformEmbedding.toIsUniformInducingproof · cited by 44
- TopologicalSpace.NonemptyCompacts.mapstatement · cited by 18
- IsUniformInducing.uniformContinuous_iffproof · cited by 17
- TopologicalSpace.NonemptyCompacts.isUniformEmbedding_coeproof · cited by 7
- TopologicalSpace.NonemptyCompacts.uniformContinuous_coeproof · cited by 4
- UniformContinuous.image_hausdorffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsUniformInducing.nonemptyCompacts_mapproof · cited by 1