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WEAK DIMENSION AND CHAIN-WEAK DIMENSION OF ORDERED SETS
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 Title & Authors
WEAK DIMENSION AND CHAIN-WEAK DIMENSION OF ORDERED SETS
KIM, JONG-YOUL; LEE, JEH-GWON;
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 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;
 Language
English
 Cited by
 References
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