The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category CONV of convergence spaces. It is well known that the category DCPO of dcpos and Scott continuous functions can be embedded into TOP, and so into CONV, by considering the Scott topology. We propose a di3erent, “cotopological” embedding of DCPO into CONV, which, in contrast to t...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

Previously we found that Parkinson's disease (PD) patients are impaired in procedural-based category learning when category membership is defined by a nonlinear relationship between stimulus dimensions, but these same patients are normal when the rule is defined by a linear relationship (Maddox and Filoteo, 2001; Filoteo et al., 2005a,b). We suggested that PD patients' impairment was due to a d...

We use continuity spaces, a common refinement of posets and metric spaces, to develop a general theory of semantic domains which includes metric spaces and domains of cpo’s as special cases and provides the appropriate tools for producing new examples which may be suitable for modeling language constructs that occur in concurrent and probabilistic programming. Our proposal for a general notion ...

in today’s turbulent world, the continuity of criticalactivities in the event of disruptions, and also fast recovery and return tobusiness as usual, are vital for sustainable success of companies. maintainingcontinuous delivery of critical business processes in the event of disruptions isa matter of business continuity. business continuity management system (bcms)is concerned with the developme...

The aim of this note is to study local and global Seshadri constants for a family of smooth surfaces with prescribed polarization. We shall first observe that given α being smaller than the square root of the degree of polarization, the set of local Seshadri constants in the range (0, α] is finite. This in particular implies that the square root of the degree of polarization is the only possibl...