It has become increasingly apparent that geometric relationships often exist between regions of two proteins that have quite different global topologies or folds. In this article, we examine whether such relationships can be used to infer a functional connection between the two proteins in question. We find, by considering a number of examples involving metal and cation binding, sugar binding, and aromatic group binding, that geometrically similar protein fragments can share related functions, even if they have been classified as belonging to different folds and topologies. Thus, the use of classifications inevitably limits the number of functional inferences that can be obtained from the comparative analysis of protein structures. In contrast, the development of interactive computational tools that recognize the "continuous" nature of protein structure/function space, by increasing the number of potentially meaningful relationships that are considered, may offer a dramatic enhancement in the ability to extract information from protein structure databases. We introduce the MarkUs server, that embodies this strategy and that is designed for a user interested in developing and validating specific functional hypotheses.