We define the Riemann integral for bounded functions defined on a general topological measure space. When the space is a compact metric space the integral is equivalent to the R-integral defined by Edalat using domain theory.

In Exact Real Arithmetic, real numbers are represented as potentially infinite streams of information units, called digits. In this paper, we work in the framework of Linear Fractional Transformations (LFT’s, also known as Möbius transformations) that provide an elegant approach to real number arithmetic (Gosper 1972, Vuillemin 1990, Nielsen and Kornerup 1995, Potts and Edalat 1996, Edalat and ...

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson’s implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bou...

In this paper we define a bisimulation concept for some very general models for stochastic hybrid systems (general stochastic hybrid systems). The definition of bisimulation builds on the ideas of Edalat and of Larsen and Skou and of Joyal, Nielsen and Winskel. The main result is that this bisimulation for GSHS is indeed an equivalence relation. The secondary result is that this bisimulation re...

The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized Q-categories by Kostanek Waszkiewicz, where Q is a commutative unital quantale. This paper concerns influence structure quantale on connection between Yoneda completeness directed their sets balls. In case that unit interval [0, 1] equipped with continuous t-norm &, it shown in order each Q-ca...

We generalize the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann to obtain computational models for separated Q-categories. We fully describe (a) Yoneda complete and (b) continuous Yoneda complete Q-categories via their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces: we show that (a) a quasi-met...