a generalization of the idea of measuring distance

a set in which we have a measure of the closeness or proximity of two elements of the set, that is, we have a distance defined on the set

a set with a global distance function (the metric ) that, for every two points in , gives the distance between them as a nonnegative real number

a space where a distance between points is defined

metric space is a set equipped with a function : Ã— â†’ satisfying the following conditions for all , , and in : (, (, if (, ) = 0 then = ( identity of indiscernibles) (, ) = (, ) ( symmetry) (, ) â‰¤ (, ) + (, ) ( triangle inequality) The function is called a metric on .

In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. The Euclidean metric of this space defines the distance between two points as the length of the straight line connecting them.