2015/01/13 by John L. Pfaltz, Pfaltz, John L.
Mathematics · #05C02 #47N02 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C02 #msc:47N02
paper · pdf · doi:10.48550/arxiv.1501.03072
15 pages. 1 figure
arxiv created 2015/01/13 · arxiv updated 2015/01/14
An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating; every dominating operator embodies a closure. Both can be the basis of continuous set transformations. Dominating operators that exhibit categorical pull-back constitute a Galois connection and must be antimatroid closure operators. Applications involving social networks and learning spaces are suggested