International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 321761, 6 pages
Continuity in Partially Ordered Sets
Department of Mathematics, University of Connecticut, Stamford, CT 06901, USA
Received 12 September 2007; Revised 8 October 2007; Accepted 4 December 2007
Academic Editor: Pentti Haukkanen
Copyright © 2008 Venu G. Menon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The notion of a continuous domain is generalized to include posets which are not dcpos and in which the set of elements way below an element is not necessarily directed. We show that several of the pleasing algebraic and topological properties of domains carry over to this setting.