Ubiquitous computing (or ambient intelligence) has been the subject of research in the mobile telecommunications field for many years. Developments such as the Internet of Services and Grid computing have complemented and strengthened this work. The ubiquitous computing paradigm integrates information processing into the objects that surround us in our environment. One particular focus has been on the development of smart spaces in homes, offices and public areas, in which automation can be used to support the user. However, these are static spaces that offer ubiquitous characteristics in a limited environment, like islands in an ocean. When the user steps outside of this island, all of this is lost. The Persist project is investigating a novel approach which combines mobile communications with the notions of these static smart spaces to produce more general ubiquitous or pervasive systems in the form of the self-improving Personal Smart Space. The vision is that a Personal Smart Space will stay with the user as he/she moves around and provide an interface between the user and the various services and sensors which are available, either directly or indirectly, as well as with other neighbouring Personal Smart Spaces. Thus Personal Smart Spaces will be able to interface to local devices and services (even when no Internet connectivity is available to the user) and to interact with other Personal Smart Spaces to create a more powerful and flexible environment for the user and one which is more truly ubiquitous.