Subcollections

Subcollections are selections drawn from a larger collection of items. In general terms, if C is a collection, a subcollection S is another collection consisting only of elements that also belong to C. The relationship is usually described by the inclusion symbol S subset of C, and the full collection C is itself a subcollection of C, as is the empty collection.

Formally, S is a subcollection of C if every element of S is an element of C. In many contexts, the emphasis is on choosing items from C according to a rule or criterion, rather than on the internal structure of the items themselves. When C has n elements, the set of all subcollections corresponds to the power collection of C, and the number of subcollections of a given size k is the binomial coefficient C(n, k).

Examples help illustrate the concept. From a library’s collection C of books, a subcollection S could be the books published in the 1990s, or the fiction titles, or the books that are currently checked out. In a database, a subcollection might consist of records that satisfy a query, such as all entries with a certain tag or attribute. In mathematics, a subcollection is often used to refer to any selection of members from a given collection, regardless of the nature of the elements.

Subcollections are widely used across disciplines, including mathematics, computer science, library science, and digital libraries. They enable focused organization and browsing by grouping relevant items while preserving the linkage to the original collection.