Mathlib Map

Theorems · Theorem · general topology

Bornology.nonempty_of_not_isBounded

∀ {α : Type u_2} {x : Bornology α} {s : Set α}, ¬Bornology.IsBounded s → s.Nonempty
Defined in
Mathlib.Topology.Bornology.Basic
Cited by
1 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AntilipschitzWith.isBounded_of_image2_left · cited by 3AntilipschitzWith.isBound…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptyBornology.IsBounded · cited by 293Bornology.IsBoundedBornology · cited by 188BornologySet.nonempty_iff_ne_empty · cited by 96Set.nonempty_iff_ne_emptyBornology.isBounded_empty · cited by 5Bornology.isBounded_emptyBornology.nonempty_of_not_isB…CITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.