In this paper we make research on the set NK of indices of convergence and the set NH n of indices of maximum density for the class of n×n symmetric imprimitive nearly reducible Boolean matrices.

We introduce almost secord countable space dlmost first count-able, almost separable spaces and almost Lindelof spaces whivh are generalizations of secord countable, first countbale seoparable and Lindelof spaces, respectively.

almost first—countable,almost separable)iff its underlying space is almost sec- ond countable (resp.

In this paper,we consider a TDS with the specification property,and a sequence of almost additive continuous functions,we define the irregular set for it(in the sense of sub-additive ergodic theorem) and show that this irregular set is either empty or carries full almost additive topological pressure.