A note on bornologies. (English) Zbl 1422.57060

Protasov, I. V.

Mat. Stud. 49, No. 1, 13-18 (2018).

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.

Reviewer: Tom Vroegrijk (Hasselt)

MSC:

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

Keywords:

bornology; uniformity; vector topology; Stone-Čech compactification; antitall ideal

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