A Half-Space Approach to Order Dimension
نویسندگان
چکیده
The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to the dimension of partially ordered sets.
منابع مشابه
ar X iv : m at h / 07 02 50 9 v 1 [ m at h . C O ] 1 7 Fe b 20 07 A half - space approach to order dimension Stephan Foldes and
The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.
متن کاملar X iv : m at h / 07 02 50 9 v 1 [ m at h . C O ] 1 7 Fe b 20 07 A half - space approach to order dimension
The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.
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ورودعنوان ژورنال:
- Order
دوره 24 شماره
صفحات -
تاریخ انتشار 2007