A note on bornologies (Q2414383)

The author defines a bornology \(\mathcal{B}\) to be antitall if for each \(Y\not\in \mathcal{B}\) there exists a \(Z\subseteq Y\) such that \(Z'\not\in \mathcal{B}\) for any \(Z'\subseteq Z\). This article contains several characterizations of antitall bornologies. It is shown, for example, that a bornology is antitall iff it is defined by a vector space topology.