On Definitions of Cuts and Completion of Partially Ordered Sets
β Scribed by Alexander Abian
- Publisher
- John Wiley and Sons
- Year
- 1968
- Tongue
- English
- Weight
- 186 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Preordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the __T__~0~(__T__~1~,
The HAHN-BANACH-theorem is known to have fundamental importance for several fields of mathematics. This theorem is not used concerning functionals, but operators which map into a real partially ordered vector space. In this paper is shown that the validity of this theorem is equivalent t o the vali
Any set throughout whole this paper will be assumed non-empty, if it will be not specially given a contrary and any order type, i.e. a type of linearly ordered set, will be assumed as a type of a set containing at bast two elements. If G is a set, then card a denotes the cardinality of G . A linearl