Topologies on products of partially ordered sets II: Ideal topologies |
| |
Authors: | Marcel Erné |
| |
Institution: | 1. Institut für Mathematik, Universit?t Hannover, Hannover, Federal Republic of Germany
|
| |
Abstract: | Within the theory of ideals in partially ordered sets, several difficulties set in which do not occur in the special case
of lattices (or bidirected posets). For example, a finite product of ideals in the factor posets need not be an ideal in the
product poset. The notion ofstrict ideals is introduced in order to remedy some deficiencies occurring in the general case of an arbitrary product of posets. Besides
other results, we show the following main theorem:
The ideal topology (cf. 2]) of a product of non-trivial posets coincides with the product topology if and only if the number
of factors is finite (4.19.).
Presented by L. Fuchs |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|