Say I have an $m$-dimensional space (continuous or discrete) such that every point in that space has a value, and that value is an $n$-dimensional vector (continuous or discrete). My question is how do I describe this space using formal mathematics, and how do I perform operations on it? "Continuous" means that the set of all positions or values in the case of the vector lie in $\mathbb{R}$ and discrete means that the set of all positions or values in the case of the vector lie in $\mathbb{Z}$ (the set of all integers). Sorry about my wording being weird, but I am asking this question exactly to clarify that/understand how I would describe such a thing.
EDIT: Another way and maybe much clearer way of describing the kind of thing I want is a hash map where there is an $m$-dimensional "continuous or discrete" set of keys which each give you an $n$-dimensional "continuous or discrete" value. This is a more "computer science-y" way of explaining what I want, but is perhaps more clear.
Also, if you can think of some more tags feel free to edit and add them.