We study the relationship between convergence spaces and convergence classes given by means of both nets and filters, we consider the duality between them and we identify in convergence terms when a convergence space coincides with a convergence class. We examine the basic operators in the Vienna Development Method of formal systems development, namely, extension, glueing, restriction, removal and override, from the perspective of the Logic for Computable Functions. Thus, we examine in detail the Scott continuity, or otherwise, of these operators when viewed as operators on the domain (X → Y) of partial functions mapping X into Y. The important override operator is not Scott continuous, and we consider topologies defined by convergence classes which rectify this situation.
Seda, A. K.,
& Hitzler, P.
(2001). Convergence Classes and Spaces of Partial Functions. Domain Theory, Logic and Computation, 75-115.