  We study the notions of acs, luacs and uacs Banach spaces which were
introduced by V. Kadets et al. in 2000 and form common generalisations of the
usual rotundity and smoothness properties of Banach spaces. In particular, we
are interested in (mainly infinite) absolute sums of such spaces. We also
introduce some new classes of spaces that lie inbetween those of acs and uacs
spaces and study their behaviour under the formation of absolute sums as well.
