User mathymathy - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T12:44:03Z http://mathoverflow.net/feeds/user/3492 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/12769/name-for-lower-upper-bounds-of-arbitrary-relations Name for "lower/upper bounds" of arbitrary relations? mathymathy 2010-01-23T20:36:47Z 2010-01-25T02:59:32Z <p>Given a partial order <em>R</em><sub>≤</sub> over a set <em>D</em>, the set of upper bounds under <em>R</em> of a subset <em>S</em> of <em>D</em> is commonly defined as { <em>y</em> ∈ <em>D</em> | ∀ <em>x</em> ∈ <em>S</em>, <em>x R y</em> }.</p> <p>(The set of lower bounds of <em>S</em> may be defined as the set of upper bounds of <em>S</em> under the converse relation <em>R</em><sup>-1</sup>)</p> <p>Is there a common name for the generalization of this notion where <em>R</em> is not a partial order, and is possibly a heterogenous relation between domain <em>D</em> and codomain <em>D'</em> (hence the <em>y</em> would be elements of the codomain)? This would be a subset of the image of <em>S</em> under <em>R</em> (and conversely, the dual notion would be a subset of the preimage).</p> http://mathoverflow.net/questions/12840/where-can-i-learn-about-master-equation/12843#12843 Answer by mathymathy for Where can I learn about master equation? mathymathy 2010-01-24T14:03:31Z 2010-01-24T14:03:31Z <p>FYI, the referenced paper seems to be SN Dorogovtsev, JFF Mendes, AN Samukhin: "Structure of growing networks with preferential linking", Physical Revew Letters 2000.</p>