Walter Scott was a Biochemistry professor at the University of Miami, Miller School of Medicine and a leading figure in the field of HIV drug resistance. His untimely passing in January 2013 marked a loss for his family, as well as for students and colleagues who knew him as a dedicated and unassuming scholar, and a lively scientist with a great sense of humor.

A dcpo P is continuous if and only if the lattice C(P ) of all Scottclosed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C(P ). In this paper, we study the order-theoretic properties of C(P ) for general dcpo’s P . The main results are: (i) every C(P ) is C-continuous; (ii) a complete lattice L is iso...

As our interactions with computing continue to expand off the desktop, we want to use mobile devices in many, if not all, of our everyday activities. However, the touch screen and physical button centric interfaces of today’s mobile devices offer relatively poor support for interaction in many situations where computing is not our primary task. For example, when wearing gloves in the cold, a mo...

Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. T...