Steinhaus– Borsuk– Lebesgue– Zorn theorem

GPTKB entity

Predicate	Object
gptkbp:instance_of	gptkb:theorem
gptkbp:applies_to	compact spaces convex sets
gptkbp:field	gptkb:Mathematics
gptkbp:has_applications_in	gptkb:analysis geometry topological spaces combinatorics
gptkbp:has_implications_for	gptkb:Continuous_Integration compactness connectedness dimension theory
https://www.w3.org/2000/01/rdf-schema#label	Steinhaus– Borsuk– Lebesgue– Zorn theorem
gptkbp:is_considered	mathematical research
gptkbp:is_debated_in	existence of certain partitions
gptkbp:is_discussed_in	academic papers mathematical textbooks
gptkbp:is_part_of	gptkb:analysis functional analysis convex analysis set-theoretic topology topological geometry
gptkbp:is_related_to	topological groups functional spaces metric spaces Banach spaces Hilbert spaces convex hulls finite-dimensional spaces Hausdorff spaces normed spaces topological vector spaces Borsuk's conjecture Lebesgue's dominated convergence theorem Zorn's lemma applications infinite-dimensional spaces
gptkbp:is_used_in	abstract algebra mathematical logic mathematical proofs theoretical mathematics applied mathematics proofs of other theorems
gptkbp:named_after	gptkb:Hugo_Steinhaus Gottlob Frege Zorn Henri Lébesgue Karol Borsuk
gptkbp:related_to	gptkb:Set gptkb:topology gptkb:analysis functional analysis Borsuk– Ulam theorem
gptkbp:uses	gptkb:Zorn's_lemma gptkb:Lebesgue_measure Borsuk's theorem
gptkbp:bfsParent	gptkb:Hugo_Steinhaus
gptkbp:bfsLayer	6