A representation theorem for recovering contraction relations satisfying wci

A Representation Theorem for Spatial Relations

Spatial relations have been investigated in various inter-related areas such as qualitative spatial reasoning (for agents moving in an environment), geographic information science, general topology, and others. Most of the results are specific constructions of spatial relations that fulfill some required properties. Results on setting up axioms that capture the desired properties of the relatio...

A Pseudo Representation Theorem for Various Categories of Relations

It is well-known that, given a Dedekind categoryR the category of (typed) matrices with coefficients from R is a Dedekind category with arbitrary relational sums. In this paper we show that under slightly stronger assumptions the converse is also true. Every atomic Dedekind category R with relational sums and subobjects is equivalent to a category of matrices over a suitable basis. This basis i...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Fuzzy implications satisfying convexity relations

It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

Steiner loops satisfying Moufang's theorem

A loop satisfies Moufang’s theorem whenever the subloop generated by three associating elements is a group. Moufang loops (loops that satisfy the Moufang identities) satisfy Moufang’s theorem, but it is possible for a loop that is not Moufang to nevertheless satisfy Moufang’s theorem. Steiner loops that are not Moufang loops are known to arise from Steiner triple systems in which some triangle ...