metric space

1. Introduction

1. Introduction

A metric space $(G, d)$ is a set with a metric $d(x,y): G \times G \rightarrow \mathbb{R}$ defined on members of the set. This metric is a generalization of distance, with the following properties:

\begin{aligned}\label{}d(x, x) = 0 \\x \ne y \implies d(x, y) > 0 \\d(x, y) = d(y, x) \\d(x, z) \le d(x, y) + d(x, z)\end{aligned}

where property $(4)$ is the triangle inequality.

metric space

Table of Contents

1. Introduction