Complexity spaces as quantitative domains of computation

We study domain theoretic properties of complexity spaces. Although the so-called complexity space is not a domain for the usual pointwise order, we show that, however, each pointed complexity space is an ¿-continuous domain for which the complexity quasi-metric induces the Scott topology, and the supremum metric induces the Lawson topology. Hence, each pointed complexity space is both a quantifiable domain in the sense of M. Schellekens and a quantitative domain in the sense of P. Waszkiewicz, via the partial metric induced by the complexity quasi-metric. © 2011 Elsevier B.V.Romaguera Bonilla, S.; Schellekens, M.; Valero Sierra, O. (2011). Complexity spaces as quantitative domains of computation. Topology and its Applications. 158:853-860. doi:10.1016/j.topol.2011.01.00585386015