Isolated point

In topology, a member of a set is an isolated point, if there is a neighborhood of in which (except) are no further elements of. A point is exactly then isolated when no accumulation point of is.

Is every point of a topological space isolated, called the room discreetly.

Examples

The following examples use subsets of the real numbers with the usual topology.

• In the crowd is an isolated point.
• The amount of each of the elements is an isolated point, but is not an isolated point.
• In the set of natural numbers all elements are isolated points. It is a discrete space.