partially ordered

English

Adjective

partially ordered (not comparable)

1. (set theory, order theory, of a set) Equipped with a partial order; when the partial order is specified, often construed with by.
   • 1963, L. V. Kantorovič, B. Z. Vulih, A. G. Pinsker, “Partially Ordered Groups and Partially Ordered Linear Spaces”, in A. L. Brudno, editor, American Mathematical Society Translations, Series 2, Volume 27: 18 papers on algebra, American Mathematical Society, page 51:

     This leads to the introduction of new kinds of abstract spaces—partially ordered linear spaces—and to their systematic use in functional analysis. The beginnings of a theory of partially ordered linear spaces are given in the works of L. V. Kantorovič in 1935-1937.

   • 1966, S. J. Taylor, Introduction to Measure and Integration, Cambridge University Press, page 22:

     The chains in ${\displaystyle {\mathcal {V}}}$ form a class ${\displaystyle {\mathcal {C}}}$ which is partially ordered by inclusion.

   • 2008, Patrik Eklund, M. Ángeles Galán, Partially Ordered Monads and Rough Sets, James F. Peters, Andrzej Skowron (editors), Transactions on Rough Sets VIII, Volume 8, Springer, LNCS 5084, page 53,

     In this paper we will show that partially ordered monads contain appropriate structure for modeling rough sets in a generalized relational setting.

Usage notes

• See notes at partially ordered set.

Derived terms

• partially ordered set

Translations