in this paper, some categorical properties of the category ${bf cpo}_{{bf act}text{-}s}$ of all {cpo $s$-acts}, cpo's equipped with actions of a monoid $s$ on them, and strict continuous action-preserving maps between them is considered. in particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. also, we show that the forgetful functor from...

We theoretically formulate the problem of processing continuous-space binary random fields by means of mathematical morphology. This may allow us to employ mathematical morphology to develop new statistical techniques for the analysis of binary random images. Since morphological transformations of continuous-space binary random fields are not measurable in general, we are naturally forced to em...

A real x is ∆1-Kurtz random (Π 1 1-Kurtz random) if it is in no closed null ∆1 set (Π 1 1 set). We show that there is a cone of Π 1 1-Kurtz random hyperdegrees. We characterize lowness for ∆1-Kurtz randomness as being ∆ 1 1-dominated and ∆ 1 1semi-traceable.