We introduce axiomatically a more general notion of a convex space dropping one axiom, the so called cancellation law. A wider class of convex sets includes in particular ordinary convex sets and semilattices. Then we introduce a notion of a topological convex space and establish for it theorems...

In the paper we give two characterizations of choice functions satisfying the outcast condition. The first one is given in order terms, and the second (algebraic) one is given in terms of an operation on the set of stable menus. We investigate implications of associativity of the operation as...

We discuss the existence of equilibria in ecomomies with indivisible goods. The reasons for which existence of equilibria obtains or not are described. We discuss previous papers on this topic whose results are based on the assumption that goods are gross substitutes. Alternatively in this paper...