We describe a way of constructing models for the continuum which does not require an underlying structure of points. With a condition of spatial homogeneity the models have the mathematical structure of a sheaf.

A recent thought experiment to achieve superluminal signalling within the Pitowsky model is examined, and it is shown that such signalling is not possible. The analysis of the experiment is used to highlight the paradoxical nonphysical nature of Pitowsky's extended notion of probability.