Topology prediction is a bioinformatics tool which assist in mapping the surface of the functional protein. But normally this functional protein is membrane protein. Why we can't do the topology prediction for proteins other than membrane proteins?
Topology describes the orientation of secondary structure elements with respect to each other. It is not related to surfaces. For membrane proteins, the topology refers to the orientation within the membrane, typically which end of a transmembrane helix is on the outer surface and which on the cytoplasmic face of the membrane. Look at 'protein topology' and 'membrane topology' in wikipedia.
Topology is a branch of mathematics. It does not have any relationship to the spatial orientation of anything. It is unfortunate that mathematical terms are used in such way.
I agree with the answer posted by Matthew, all the proteins have a certain topology which defines the functionality in terms of a its own activity, interactions made by it or topology variation governed by other partner biomolecules. It is a mathematical term to define the elements and their local as well as global connectivities in the protein or nucleic acid molecules.