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Continuous Domains with Approximating Mappings and their Uniformity
by
Ralph Kummetz
Institute of Algebra, Dresden University of Technology, Germany
An approximating F-poset (D, <= , F) consists of a poset (D, <= ) and a directed family F of monotone mappings below the identity with supF=idD such that for all f in F there is g in F with f <= g o g. F-posets give rise to a uniformity whose properties are closely related to properties of (D, <= ) and F. We show that (D, <= ) is a continuous dcpo such that f(d) << d for all d in D and all f in F if and only if each monotone net in D converges with respect to the uniform topology. Moreover, we prove that a pointed poset is a FS-domain if and only if it arises as an approximating F-poset whose uniform topology is compact. In this case, we also derive that the uniform topology coincides with the Lawson-topology of the domain.
Date received: June 1, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-32.