Mathlib Map

Theorems · Theorem · general topology

IsUniformInducing.uniformContinuous

∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
  IsUniformInducing f → UniformContinuous f
Defined in
Mathlib.Topology.UniformSpace.UniformEmbedding
Cited by
35 results in Mathlib
Foundations
Depth 64 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.

AbstractCompletion.uniformContinuous_coe · cited by 8AbstractCompletion.unifor…TopologicalSpace.Closeds.uniformContinuous_coe · cited by 5Closeds.uniformContinuous…TopologicalSpace.NonemptyCompacts.uniformContinuous_coe · cited by 4NonemptyCompacts.uniformC…TopologicalSpace.Compacts.uniformContinuous_coe · cited by 4Compacts.uniformContinuou…Filter.totallyBounded_map_iff · cited by 2Filter.totallyBounded_map…ContinuousMultilinearMap.uniformContinuous_coe_fun · cited by 2ContinuousMultilinearMap.…IsDenseInducing.isUniformInducing_extend · cited by 1IsDenseInducing.isUniform…ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap · cited by 1ContinuousAlternatingMap.…IsUniformInducing.compacts_map · cited by 1IsUniformInducing.compact…IsUniformInducing.isUniformAddGroup · cited by 1IsUniformInducing.isUnifo…IsUniformInducing.isUniformGroup · cited by 1IsUniformInducing.isUnifo…TopologicalSpace.NonemptyCompacts.uniformContinuous_singleton · cited by 1NonemptyCompacts.uniformC…IsUniformInducing.nonemptyCompacts_map · cited by 1IsUniformInducing.nonempt…EMetric.controlled_of_isUniformInducing · cited by 1EMetric.controlled_of_isU…TopologicalSpace.NonemptyCompacts.uniformContinuous_toCloseds · cited by 1NonemptyCompacts.uniformC…UniformSpace · cited by 2040UniformSpaceUniformContinuous · cited by 410UniformContinuousIsUniformInducing · cited by 128IsUniformInducingisUniformInducing_iff' · cited by 5isUniformInducing_iff'IsUniformInducing.uniformCont…CITED BYCITES

Cites4

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

Cited by35

Results whose statement or proof uses this declaration.