TY - JOUR
AU - Pajoohesh, Homeira
PY - 2022/04/01
Y2 - 2023/10/02
TI - Representations of bornologies
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 23
IS - 1
SE -
DO - 10.4995/agt.2022.16405
UR - https://ojs.upv.es/index.php/AGT/article/view/16405
SP - 17-30
AB - <p>Bornologies abstract the properties of bounded sets of a metric space. But there are unbounded bornologies on a metric space like $\mathcal{P}(\RR)$ with the Euclidean metric. <br />We show that by replacing $[0,\infty)$ with a partially ordered monoid every bornology is the set of bounded subsets of a generalized metric mapped into a partially ordered monoid. We also prove that the set of bornologies on a set is the join completion of the equivalence classes of a relation on the power set of the set.</p>
ER -