Is there a picture which portrays how function spaces are related to each other? After searching on the web, I could not find a picture portraying how functions' classes are related to each other. With function classes, I mean for instance continuous, differentiable, regulated functions...
For example, when it comes to classes of vector spaces the attached image portrays how Metric, Normed, Banach, and Hilbert spaces relate to each other as subsets of each other.



Does anyone know of an image that describes which function classes are subsets of other function classes? E.g. As far as I know the space of continuous functions is a subset of the space of regulated functions.
 A: I'm not entirely sure if this is what you are looking for since the following concerns the relation between different function spaces of the same family, not necessarily different families, but maybe it's helpful nonetheless.
There is this very nice diagram from this blog post by Terence Tao. It relates various function spaces according to their regularity and integrability parameter (see the blog post linked above for more info - it's really worth checking out regardless). Generally speaking, spaces higher up on the vertical scale are contained in those which are lower down. In the horizontal direction, the inclusions depend on the underlying (metric) space.

There are also diagrams relating Sobolev spaces of different types such as this one from this Wikipedia entry on the Sobolev inequalities.

In principle, you can make this sort of diagram for any families of function spaces whenever there are embedding theorems like Sobolev (and Hölder) spaces as above, but also Campanado-Morrey spaces or Besov spaces.
