A Helly family of order is a set family for which every finite subfamily has nonempty total intersection whenever each of its subfamilies with at most members has nonempty intersection. Convex subtrees of a tree have Helly order two.
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The term "Helly family" may refer to a variety of subjects depending on context, but it does not appear to have a widely recognized or specific meaning. It could be the name of a family or clan that may be associated with historical, cultural, or genealogical significance. If you're referring to a specific Helly family known for something (like in media, history, etc.