Metric Space

A metric space is a mathematical formalization of space. So a metric space is a set elements called points. Each point is said to have a distance between them. The notion of what distance means differentiates different metric spaces.

Some popular metric spaces are:

• Euclidean Space
• Complex numbers
• Real numbers

Mathematical Definition

A Metric space in an ordered pair $(M,d)$ where

• $M\to$ Set of elements (points).
• $d\to$ distance function (metric) is defined as

$$d:X\times X\to \mathbb{R}$$

Here the distance functions takes two elements from $M$ and maps it to a single real number which is supposed to represent the distance between the two points.