Related Notions
A subset of a partially ordered set is said to be cofinal if for every there exists some such that . Every cofinal subset of a partially ordered set with maximal elements must contain all maximal elements.
A subset of a partially ordered set is said to be a lower set of if it is downward closed: if and then . Every lower set of a finite ordered set is equal to the smallest lower set containing all maximal elements of .
Read more about this topic: Maximal Element
Famous quotes containing the words related and/or notions:
“One does not realize the historical sensation as a re-experiencing, but as an understanding that is closely related to the understanding of music, or rather of the world by means of music.”
—Johan Huizinga (1872–1945)
“Assumptions that racism is more oppressive to black men than black women, then and now ... based on acceptance of patriarchal notions of masculinity.”
—bell hooks (b. c. 1955)