 Many of the examples below can be seen as concrete versions of this general idea.Every metric space is a topological space in a natural manner, and therefore all definitions and theorems about general topological spaces also apply to all metric spaces.About any point formula_15 in a metric space formula_2 we define the open ball of radius formula_78 (where formula_79 is a real number) about formula_15 as the set
These open balls form the base for a topology on "M", making it a topological space.