Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...

The domain theoretic notion of lifting allows one to extend a partial order in a trivial way by a minimum. In the context of Quantitative Domain Theory (e.g. [BvBR98] and [FK93]) partial orders are represented as quasi-metric spaces. For such spaces, the notion of the extension by an extremal element turns out to be non trivial. To some extent motivated by these considerations, we characterize ...

Let P (S) denote the space of projective structures on a closed surface S. It is known that the subset Q(S) P (S) of projective structures with quasiFuchsian holonomy has in nitely many connected components. In this paper, we investigate the con guration of these components. In particular, we show that the closure of any exotic component of Q(S) intersects the closure of the standard component ...