Spatially Localised Membrane Systems

In this paper we investigate the use of general topological spaces in connection with a generalised variant of membrane systems. We provide an approach which produces a fine grain description of local operations occurring simultaneously in sets of compartments of the system by restricting the interactions between objects. This restriction is given by open sets of a topology and multisets of objects associated with them, which dynamically change during the functioning of the system and which together define a notion of vicinity for the objects taking part in the interactions.