Topology in information theory in topology

We prove that timed capacity in information theory is a Euclidean continuous function of noise. This is a result based on topological methods that benefits work in information theory. Then we show that binary timing capacity is a measure of distance which yields the Euclidean topology on the unit interval, despite the fact that it does not satisfy the triangle inequality. This is a result based on information theoretic methods that benefits topology. These results have important applications in an area known as information hiding, in the study of quantum communication and in domain theory. They appear to raise fundamental questions about the nature of distance itself.