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A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for ...

A set in which no element divides the sum of any nonempty subset of the other elements. For example, {2,3,5} is dividing, since 2|(3+5) (and 5|(2+3)), but {4,6,7} is ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

The Schröder-Bernstein theorem for numbers states that if n<=m<=n, then m=n. For sets, the theorem states that if there are injections of the set A into the set B and of B ...

The upper irredundance number IR(G) of a graph G is the maximum size of an irredundant set of vertices in G. It is therefore equal to the size of a maximum irredundant set as ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

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 ...

An independent edge set (also called a matching) of a graph G is a subset of the edges such that no two edges in the subset share a vertex of G (Skiena 1990, p. 219). The ...

The (lower) irredundance number ir(G) of a graph G is the minimum size of a maximal irredundant set of vertices in G. The upper irredundance number is defined as the maximum ...