We introduce a new general polynomial-time constructionthe fibre constructionwhich reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P ), where P is any subprojective relational structure. As a consequence we get a new proof (not using universal algebra) that CSP(P ) is NP -complete for any subprojective (and so for any projective) relational structur...

The topography associated with the fundamental crustal dichotomy in much of eastern Mars can be largely ascribed to a single event: the very large impact which produced the Utopia Basin. Subsequent internal and surficial processes have been unable to remove the topographic signature of this basin. In particular, endogenic processes appear to have been ineffective in contributing to the basic di...

The Schnorr-Stimm dichotomy theorem (Schnorr and Stimm, 1972) concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet Σ. asserts that, for any such sequence S, the following two things are true. (1) If S is not normal in sense Borel (meaning every strings equal length appear with asymptotic frequency S), then there gambler wins money at an infinitel...

Let R be a ring equipped with proper norm. We show that under suitable conditions on R, there is natural basis continuous linear injection for the set of Polish R-modules which are not countably generated. When division ring, this can taken to singleton.