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A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.

A set S with a single point P removed is called a punctured set, written S\{P}.

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

The Mandelbar set is a fractal set analogous to the Mandelbrot set or its generalization to a higher power with the variable z replaced by its complex conjugate z^_.

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

A Julia set J consisting of a set of isolated points which is formed by taking a point outside an underlying set M (e.g., the Mandelbrot set). If the point is outside but ...

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 ...

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The set difference A\B is defined by A\B={x:x in A and x not in B}. Here, the backslash symbol is defined as Unicode U+2216. The set difference is therefore equivalent to the ...