We introduce a foundational language for modelling applications over global computers whose interconnection structure can be explicitly manipulated. Together with process distribution, mobility, remote operations and asynchronous communication through distributed data spaces, the language provides constructs for explicitly modelling inter-node connections and for dynamically establishing and removing them. For the proposed language, we define natural notions of extensional observations and study their closure under operational reductions and/or language contexts to obtain barbed congruence and may testing equivalence. For such equivalences, we provide alternative characterizations in terms of a labelled bisimulation and a trace equivalence that can be used for actual proofs.