definition. standard Peano space [fauser2002treatise] [hopf-0004]

✍️source

A standard Peano space is a Peano space over the linear space \(V\) of dimension \(n\) whose bracket has the additional property that for every vector \(x \in V\) there exist vectors \(x_2, \ldots , x_n\) such that \[ \left [x, x_2, \ldots , x_n\right ] \neq 0 . \]

In such a space the length of the bracket, i.e. the number of entries, equals the dimension of the space, and conversely. We will be concerned here with standard Peano spaces only.