A note on bornologies. (English) Zbl 1422.57060

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.


57N17 Topology of topological vector spaces
46A17 Bornologies and related structures; Mackey convergence, etc.
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