Metric space

• categories: Real Analysis, Definition

Definition :

Set with the Metric

Examples

• $\mathbb{R}$ with $d(x,y)=|x-y|$
• ${\mathbb{R}}^n$ with $d(\bar{x},\bar{y})=\sqrt{\sum (x_i-y_i{)}^2}$ - default Euclidean metric
• ${\mathbb{R}}^2$ with $d(\bar{x},\bar{y})=\sum |x_i-y_i|$