Point set in the context of "Primitive notion"

In geometry, a set of points is convex if it contains every line segment between two points in the set.For example, a solid cube is a convex set, but anything that is hollow or has an indent, such as a crescent shape, is not convex.

The boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a given subset A of Euclidean space is called the convex hull of A. It is the smallest convex set containing A.

In mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S and there exists a neighborhood of x that does not contain any other points of S. This is equivalent to saying that the singleton {x} is an open set in the topological space S (considered as a subspace of X). Another equivalent formulation is: an element x of S is an isolated point of S if and only if it is not a limit point of S.

If the space X is a metric space, for example a Euclidean space, then an element x of S is an isolated point of S if there exists an open ball around x that contains only finitely many elements of S.A point set that is made up only of isolated points is called a discrete set or discrete point set (see also discrete space).