what's mean metric space?

Answer 1

mathematics, a metric space is a set where a notion of distance (called a metric) 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. The geometry of the space depends on the metric chosen, and by using a different metric we can construct interesting non-Euclidean geometries such as those used in the theory of general relativity.

Answer 2

A metric space is a set X along with a function d:XxX-->R with he following properties:

1) d(x,y)>=0 for all x,y in X
2) d(x,y)=0 if and only if x=y
3) d(x,y)=d(y,x) for all x and y in X
4) d(x,z)<=d(z,y)+d(y,z) for all x,y, and z in X.

We call d(x,y) the distance from x to y.

Answer 3

You need more help with English than you do with math.