The bounded-complete hull of an &agr;-space
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
A computational model for metric spaces
Theoretical Computer Science
Lawson topology of the space of formal balls and the hyperbolic topology
Theoretical Computer Science
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K. Martin and P. Panangaden [Martin, K., and P. Panangaden, A domain of space-time intervals in general relativity, Communications in Mathematical Physics, 267 (2006), pages 563-586] have made the interesting observation that the causal order in general relativity theory closely relates to domain theoretical notions. From the causal structure of models of space-time which are called strongly hyperbolic they extract the notion of a strongly hyperbolic poset. These are in particular bicontinuous, that is, continuous posets with the property that they are also continuous with respect to the opposite order. Not much is known about bicontinuous posets. In this paper we collect known results, we exhibit substantial examples, we show that these examples are connected with open problems in domain theory, and we indicate directions of research.