Weak dimension and chain-weak dimension of ordered sets

Abstract

In this paper, we define the weak dimension and the chain-weakdimension of an ordered set by using weak orders and chain-weakorders, respectively, as realizers. First, we prove that if P isnot a weak order, then the weak dimension of P is the same asthe dimension of P. Next, we determine the chain-weak dimensionof the product of k-element chains. Finally, we prove someproperties of chain-weak dimension which hold for