On the Kocinac alpha_i properties

Boaz Tsaban

Published 2006-07-24, updated 2010-11-04Version 4

The Kocinac alpha_i properties, i=1,2,3,4, are generalizations of Arhangel'skii's alpha_i 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 Kocinac.