Euclidean Spaces

We want to study multivariate functions (i.e., functions of many variables), continuous multivariate functions in particular. To define continuity, we need a measure of "closeness" between points. One measure of closeness is the Euclidean distance. The set R^n (n-dimensional space) with the Euclidean distance function is called a Euclidean space. This is the space where the functions of our interests live.