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Theorems · Theorem · general topology

Filter.TotallyBounded.mono

∀ {α : Type u} [uniformSpace : UniformSpace α] {f g : Filter α}, f ≤ g → g.TotallyBounded → f.TotallyBounded
Defined in
Mathlib.Topology.UniformSpace.Cauchy
Cited by
6 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
UniformSpace
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Around this declaration

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

Filter.totallyBounded_iSup · cited by 2Filter.totallyBounded_iSupFilter.totallyBounded_iff_filter · cited by 2Filter.totallyBounded_iff…Filter.totallyBounded_iff_ultrafilter · cited by 1Filter.totallyBounded_iff…Ultrafilter.cauchy_of_totallyBounded · cited by 0Ultrafilter.cauchy_of_tot…Filter.totallyBounded_comap · cited by 0Filter.totallyBounded_com…Filter.TotallyBounded.exists_clusterPt · cited by 0TotallyBounded.exists_clu…Set · cited by 53352SetFilter · cited by 8121FilterUniformSpace · cited by 2040UniformSpaceuniformity · cited by 765uniformitySetRel · cited by 581SetRelSetRel.preimage · cited by 56SetRel.preimageFilter.TotallyBounded · cited by 24Filter.TotallyBoundedTotallyBounded.monoCITED BYCITES

Cites7

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

Cited by6

Results whose statement or proof uses this declaration.