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Theorems · Theorem · general topology

CauchyFilter.mem_uniformity

∀ {α : Type u} [inst : UniformSpace α] {s : Set (CauchyFilter α × CauchyFilter α)},
  s ∈ uniformity (CauchyFilter α) ↔ ∃ t ∈ uniformity α, CauchyFilter.gen t ⊆ s
Defined in
Mathlib.Topology.UniformSpace.Completion
Cited by
1 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpace
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CauchyFilter.mem_uniformity' · cited by 0CauchyFilter.mem_uniformi…Set · cited by 53352SetFilter · cited by 8121FilterUniformSpace · cited by 2040UniformSpaceuniformity · cited by 765uniformitySetRel · cited by 581SetRelCauchyFilter · cited by 19CauchyFilterFilter.mem_lift'_sets · cited by 10Filter.mem_lift'_setsCauchyFilter.gen · cited by 6CauchyFilter.genCauchyFilter.monotone_gen · cited by 3CauchyFilter.monotone_genCauchyFilter.mem_uniformityCITED BYCITES

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Cited by1

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