[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2005.42.2.315

WEAK DIMENSION AND CHAIN-WEAK DIMENSION OF ORDERED SETS

KIM, JONG-YOUL (DEPARTMENT OF MATHEMATICS, SOGANG UNIVERSITY)
LEE, JEH-GWON (DEPARTMENT OF MATHEMATICS, SOGANG UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 315-326 More about this Journal

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.

Keywords

weak order; chain-weak order; weak dimension; chain-weak dimension;

Citations & Related Records

Reference

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