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Theorems · Theorem · general topology

Subtype.isComplete_iff

∀ {α : Type u} [inst : UniformSpace α] {p : α → Prop} {s : Set { x // p x }},
  IsComplete s ↔ IsComplete (Subtype.val '' s)

Sets of a subtype are complete iff their image under the coercion is complete.

Defined in
Mathlib.Topology.UniformSpace.UniformEmbedding
Cited by
0 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpace
Mathlib docsSourceLoogleLeanSearch

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Set · cited by 53352SetSet.image · cited by 5609Set.imageUniformSpace · cited by 2040UniformSpaceIsComplete · cited by 68IsCompleteisUniformEmbedding_subtype_val · cited by 9isUniformEmbedding_subtyp…IsUniformEmbedding.isComplete_iff · cited by 1IsUniformEmbedding.isComp…Subtype.isComplete_iffCITED BYCITES

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