- WEAK DIMENSION AND CHAIN-WEAK DIMENSION OF ORDERED SETS
- KIM, JONG-YOUL ; LEE, JEH-GWON ;
- Bulletin of the Korean Mathematical Society, volume 42, issue 2, 2005, Pages 315~326
- DOI : 10.4134/BKMS.2005.42.2.315

Abstract

In this paper, we define the weak dimension and the chain-weak dimension of an ordered set by using weak orders and chain-weak orders, respectively, as realizers. First, we prove that if P is not a weak order, then the weak dimension of P is the same as the dimension of P. Next, we determine the chain-weak dimension of the product of k-element chains. Finally, we prove some properties of chain-weak dimension which hold for dimension.