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Theorems · Theorem · general topology

AbstractCompletion.continuous_extend

∀ {α : Type uα} [inst : UniformSpace α] (pkg : AbstractCompletion.{vα, uα} α) {β : Type uβ} [inst_1 : UniformSpace β]
  {f : α → β} [CompleteSpace β], Continuous (pkg.extend f)
Defined in
Mathlib.Topology.UniformSpace.AbstractCompletion
Cited by
5 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpaceCompleteSpace
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Around this declaration

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

UniformSpace.Completion.continuous_extension · cited by 4Completion.continuous_ext…AbstractCompletion.continuous_map · cited by 3AbstractCompletion.contin…AbstractCompletion.extend_comp_coe · cited by 1AbstractCompletion.extend…AbstractCompletion.extend_map · cited by 1AbstractCompletion.extend…AbstractCompletion.extend_unique · cited by 1AbstractCompletion.extend…Continuous · cited by 2592ContinuousCompleteSpace · cited by 2532CompleteSpaceUniformSpace · cited by 2040UniformSpaceUniformContinuous.continuous · cited by 66UniformContinuous.continu…AbstractCompletion.space · cited by 41AbstractCompletion.spaceAbstractCompletion · cited by 41AbstractCompletionAbstractCompletion.uniformStruct · cited by 30AbstractCompletion.unifor…AbstractCompletion.extend · cited by 12AbstractCompletion.extendAbstractCompletion.uniformContinuous_extend · cited by 5AbstractCompletion.unifor…AbstractCompletion.continuous…CITED BYCITES

Cites9

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Cited by5

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