Bornologies, selection principles and function spaces

We study some closure-type properties of function spaces endowed with the new topology of strong uniform convergence on a bornology introduced by Beer and Levi in 2009. The study of these function spaces was initiated in [G. Beer, S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350 (2009) 568–589] and [A. Caserta, G. Di Maio, Lʼ. Holá, Arzelàʼs Theorem and strong uniform convergence on bornologies, J. Math. Anal. Appl. 371 (2010) 384–392]. The properties we study are related to selection principles.