Function spaces
The set of all functions from X to Y is denoted [X
® Y]. Such a set is called a
function space. Examples:
-
[Time ® Pressure] is the set
of all sound signals with domain Time and range Pressure.
-
[HorizontalSpace ´ VerticalSpace
® Intensity 3] is
the set of all color images of a certain domain and intensity range.
Since function spaces are just sets, we can define functions that have
function spaces as their domain, range, or both.