adherent point

On Real Line

is adherent to if s.t. .

e.g.

• is adherent to
• The supremum is adherent to

In Metric Space

Let be a metric space, let , and let be a point in . We say that is an adherent point of if for every radius the ball has a non-empty intersection with . The set of all adherent points of is called the closure of and is denoted as .

The following statements are logically equivalent:

• is an adherent point in
• is either an interior point or a boundary point of
• There exists a sequence in which converges to with respect to the metric