In this paper, we introduce and investigate the notions of Iω -continuous maps and Iω -irresolute maps in ideal topological spaces. Also we introduce the notions of slc*-I -sets, s -sets, λs - I -closed sets, slc* - I -continuous maps and λs - I -continuous maps. Finally, we obtain the decompositions of  -continuity.
In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a ::: topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.