KnowraBounded setLinked fromLinked fromThe 11 pages that link to Bounded set, each with the reason it gives.All 11Related 8Narrower topic 1Compared with 2SupremumRelated: Being bounded above is necessary, but does not by itself ensure a supremum within the space.Extreme value theoremRelated: Boundedness is the other part of that characterization in Euclidean space.Lipschitz continuityRelated: On bounded domains, a Lipschitz function has bounded output variation.Bolzano–Weierstrass theoremRelated: Boundedness prevents the sequence from escaping every finite region.Heine–Borel theoremRelated: Boundedness supplies the second condition in the theorem’s Euclidean compactness criterion.Compact operatorRelated: Compact operators are defined by how they transform every bounded set.Upper boundRelated: A set is bounded above precisely when it has at least one upper bound.Hopf–Rinow theoremRelated: Boundedness is the other condition in the theorem’s compactness characterization.