examples of metric spaces

The aim of this entry is to list metric spaces that have astandard metric.

Distance on set

• Euclidean metric on ${ℝ}^n$ and on open subsets of ${ℝ}^n$,

• Normed vector spaces,

• Hausdorff metric on sets

• Valuated field, i.e. a field and its valuation

Function spaces

• $L^p$ functions (http://planetmath.org/LpSpace)

• $𝒪(G)$; holomorphic functions (http://planetmath.org/SpaceOfAnalyticFunctions)

• $𝒮$; theSchwartz space of rapidly decreasing functions (http://planetmath.org/SpaceOfRapidlyDecreasingFunctions)