subset

Etymology

sub- + set.

noun

1. (set theory, of a set S) A set A such that every element of A is also an element of S.
   The set of integers is a subset of the set of real numbers.
   The set {a,b} is a both a subset and a proper subset of {a,b,c} while the set {a,b,c} is a subset of {a,b,c} but not a proper subset of {a,b,c}.
   1963, David B. MacNeil, Modern Mathematics for the Practical Man, David Van Nostrand, Republished as 2013, David B. MacNeil, Fundamentals of Modern Mathematics: A Practical Review, Dover, page 3, In the foregoing example, the set D of the first four letters of the alphabet, was a subset of the set A of all the letters of the alphabet, because A includes all the members of D.
   Let A be a subset of the topological space X and take x∈X. 1997, Wolfgang Filter, K. Weber, Integration Theory, Chapman & Hall, page 5
   We say that a set S has a finite partition into subsets S_1,…,S_n, if S=S_i∪…∪S_n, where the subsets are pairwise disjoint, that is, S_i∩S_j= empty , if i ne j. (We do not require that the subsets be nonempty.) 2007, Judith D. Sally, Paul J. Sally, Jr., Roots to Research: A Vertical Development of Mathematical Problems, American Mathematical Society, page 280
2. A group of things or people, all of which are in a specified larger group.
   We asked a subset of the population of the town for their opinion.

verb

1. (transitive) To take a subset of.
2. (transitive, computing, typography) To extract only the portions of (a font) that are needed to display a particular document.