We establish a monotonicity principle for convex functions that enables high-level reasoning about capacity in information theory. Despite its simplicity, this single idea is remarkably applicable.â€¦ (More)

We introduce the measurement idea in domain theory and then apply it to establish two fixed point theorems. The first is an extension of the Scott fixed point theorem which applies to nonmonotonicâ€¦ (More)

We study the algebraic structure of the monoid of binary channels and show that it is dually isomorphic to the interval domain over the unit interval with the operation from [3]. We show that theâ€¦ (More)

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countableâ€¦ (More)

Many fishes have independently evolved beach spawning with oviposition at the water's edge. These include intertidal, subtidal, and estuarine, as well as a few freshwater, species. Their spectacularâ€¦ (More)

In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scottâ€¦ (More)

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. Thenwe showâ€¦ (More)

We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximalâ€¦ (More)