Domination and Closure
Combinatorics
2015-01-14 v1
Abstract
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
Cite
@article{arxiv.1501.03072,
title = {Domination and Closure},
author = {John L. Pfaltz},
journal= {arXiv preprint arXiv:1501.03072},
year = {2015}
}
Comments
15 pages. 1 figure