## 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.

### MSC:

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

### References:

 [1] R. Engelking, General Topology, 2nd edition, PWN, Warszawa, 1985. [2] H. Hogbe-Nlend, Les racines historiques de la bornologie moderne, Seminare Choquet, 10 (1970-71), №1, 1-7. · Zbl 0243.46004 [3] I. Protasov, Varieties of coarse spaces, Axioms, 2018, 7, 32. [4] I. Protasov, M. Zarichnyi, General Asymptology, Math. Stud. Monogr. Ser., V.12, VNTL, Lviv, 2007, 219 p. [5] J. Roe, Lectures on Coarse Geometry, AMS University Lecture Ser, V.31, Providence, R.I., 2003, 176 p.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.