Knowability as continuity: a topological account of informational dependence

We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it is compatible with functional (but non-continuous) dependence. We then proceed to study a stronger notion of knowability based on uniformly continuous dependence. On the technical logical side, we determine the complete logics of languages that combine general functional dependence, continuous dependence, and uniformly continuous dependence.