Partial maps are of great interest when considering problems in mathematical economics, because they are very useful for the application of agents. Tastes of agents on a space \(X\) are usually represented by a preference relation on \(X\), that is, a subset \(R\) of \(X \times Y\), where \((x,y)\, e\, R\) means the agent prefers alternative \(x\) to \(y\). Similarities of agents then can be described by a convergence or topology on partial maps. The authors give a new definition of convergence of partial maps and its initial description amounts to bornological convergence of the associated net of graphs as defined by Lechicki, Levi and Spakowski with respect to a natural bornology on \(X \times Y\). The presented treatise involve bornologies as well as macroscopic structures considered over the last 25 years to describe convergence of nets or sequences of sets also known as bounded Hausdorff-convergence. At last the authors look at uniformizability and metrizability of its induced convergence. But they do not attempt to find general necessary and sufficient conditions for the convergence to be topological. Instead of this there is given a reference to a corresponding study of Beer, Costantini and Levi.