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A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

A set S of positive integers is said to be Diophantine iff there exists a polynomial Q with integral coefficients in m>=1 indeterminates such that ...

A set of elements S is said to be infinite if the elements of a proper subset S^' can be put into one-to-one correspondence with the elements of S. An infinite set whose ...

For a partial order, the size of the longest chain is called the length.

For a partial order, the size of the longest antichain is called the width.

Every totally ordered set (A,<=) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski ...

A semialgebraic set is a subset of R^n which is a finite Boolean combination of sets of the form {x^_=(x_1,...,x_n):f(x^_)>0} and {x^_:g(x^_)=0}, where f and g are ...

A subset E of a topological space S is said to be meager if E is of first category in S, i.e., if E can be written as the countable union of subsets which are nowhere dense ...

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...