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...

In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also closed under the boolean operations (complementation, finite unions and finite intersections). We ...

a r t i c l e i n f o a b s t r a c t Euler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Sets are represented by closed curves in the plane and often have wellformedness conditions placed on them in order to enhance comprehensibility. The theoretical underpinning for tool support has usually focussed on the problem of generating an...

In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.