We extend the expressive power of the region connection calculus RCC-8 by allowing to apply the 8 binary relations of RCC-8 not only to atomic regions but also to Boolean combinations of them. It is shown that the statisfiability problem for the extended language in arbitrary topological spaces is still in NP; however, it becomes PSPACE-complete if only the Euclidean spaces Rn , n > 0, are rega...

We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z of the Jordan curve theorem and to extend to a quite large class of locally finite metric spaces (containing all finite metric spaces) an inequality for the l-distortio...

The aim of this paper is to prove Theorem 1.1 below, a generalization to virtually nilpotent spaces of a result of Wilkerson [13] and Sullivan [12]. We recall that a CW complex Y is virtually nilpotent if (i) Y is connected, (ii) 7r~ Y is virtually nilpotent (i.e. has a nilpotent subgroup of finite index) and (iii) for every integer n > 1, zr~Y has a subgroup of finite index which acts nilpoten...