partially ordered
From Wiktionary, the free dictionary
Adjective
partially ordered (not comparable)
- (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 form a class 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
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