Bornologies, selection principles and function spaces

AbstractWe 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

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update