Home›Sources›Union-Closed Sets Conjecture (Wikipedia)SourcesUnion-Closed Sets Conjecture (Wikipedia)Encyclopedia ArticleCitation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Union-Closed Sets Conjecture (Wikipedia)." Accessed August 30, 2026. https://dev-mathematics.interactiveatlas.org/sources/wikipedia-union-closed-sets-conjecture.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Union-Closed Sets Conjecture (Wikipedia). Retrieved August 30, 2026, from https://dev-mathematics.interactiveatlas.org/sources/wikipedia-union-closed-sets-conjectureCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-union-closed-sets-conjecture-wikipedia, author = {Mathematics Atlas}, title = {Union-Closed Sets Conjecture (Wikipedia)}, year = {2026}, url = {https://dev-mathematics.interactiveatlas.org/sources/wikipedia-union-closed-sets-conjecture}, note = {Accessed August 30, 2026} }Copy BibTeXReference and ClassificationDevelopingThe Wikipedia article on the union-closed sets conjecture (Frankl's conjecture), covering its 1979 origin, the proven special cases, and Gilmer's 2022 partial-progress bound.FactsSourcesClaims Backed By This Source (23 claims)Comments (0)Reader Challenges (0 open reader challenges)FactsCitationPublisherWell-attestedWikipediaURLWell-attestedhttps://en.wikipedia.org/wiki/Union-closed_sets_conjectureSource TypeWell-attestedEncyclopediaAssessmentReliability TierWell-attested2SourcesUnion-Closed Sets Conjecture (Wikipedia)tier 2WikipediaView the SourceClaims Backed By This Source (23 claims)This source backs 23 claims across the atlas. As facts: 16 well-attested. As cited relationships: 2 holds, 1 connected. Plus 4 entities citing it as a general reference with no single fact or relationship attached.Disposition By TopicConjectures, 11 claims: 6 well-attested, 2 holds, 3 general references.Open Questions, 8 claims: 6 well-attested, 1 connected, 1 general references.Sources, 4 claims: 4 well-attested.Well-attested16ConjecturesUnion-Closed Sets ConjectureOpen QuestionsDoes every finite union-closed family of sets, other than the family holding only the empty set, really contain an element belonging to at least half of the sets in the family?SourcesUnion-Closed Sets Conjecture (Wikipedia)Holds2ConjecturesUnion-Closed Sets ConjectureConnected1Open QuestionsDoes every finite union-closed family of sets, other than the family holding only the empty set, really contain an element belonging to at least half of the sets in the family?General References4ConjecturesUnion-Closed Sets ConjectureOpen QuestionsDoes every finite union-closed family of sets, other than the family holding only the empty set, really contain an element belonging to at least half of the sets in the family?Comments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0 open reader challenges)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.View At A Past YearThe atlas records no dated fact of its own for this entry, so there is no other year to choose.Show This Year