On the Kočinac

The Kočinac αi properties, i = 1, 2, 3, 4, are generalizations of Arhangel’skĭı’s αi local properties. We give a complete classification of these properties when applied to the standard families of open covers of topological spaces or to the standard families of open covers of topological groups. One of the latter properties characterizes totally bounded groups. We also answer a question of Kočinac.