Completeness (Order Theory)

Completeness (Order Theory)

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Description

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set. A special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions of completeness exist. The motivation for considering completeness properties derives from the great importance of suprema to the theory of partial orders. Finding a supremum means to single out one distinguished least element from the set of upper bounds. On the one hand, these special elements often embody certain concrete properties that are interesting for the given application. On the other hand, the knowledge that certain types of subsets are guaranteed to have suprema or infima enables us to consider the computation of these elements as total operations on a partially ordered set. For this reason, posets with certain completeness properties can often be described as algebraic structures of a certain kind. In addition, studying the properties of the newly obtained operations yields further interesting subjects.show more

Product details

  • Paperback | 84 pages
  • 152 x 229 x 5mm | 136g
  • Fidel
  • United States
  • English
  • 6136720493
  • 9786136720494