ABSTRACT
We will again use the symbol X in all that follows to represent any of the spaces R, C, or Rk in those situations where the result may apply to any of those spaces. Related to this, we use the symbol D to denote the generic domain of a function, where D is to be understood as a nonempty subset of X. In specific examples or results, we will use the more specific notation D1
when the domain lies in R, D when the domain lies in C, and the notation Dk when the domain lies in Rk. In a similar fashion to our use of the symbols X and D, we use the notation Y to denote the codomain of a function, where Y should be interpreted as a subset (possibly a proper subset!) of any of the spaces R, C, or Rp for integer values p ≥ 2. Note that we use the letter p to denote the dimension of Rp associated with the symbol Y, since the use of the letter k is reserved for the space Rk associated with the symbol X. Also, recall that the norm notation | · | will be used for all of the spaces of interest. Finally, as usual, when results do not apply to all the spaces R, C, Rk, and Rp, we will refer to the relevant spaces explicitly.
