Study of RL-Connectedness and RL-Compactness

In this paper, we introduce a new kind of locally closed sets called regular locally closed sets (briefly RL-closed sets) in a topological space which are weaker than the locally closed sets. Regular locally continuous maps and regular locally irresolute maps are also introduced and studied some of their properties. Finally, we introduce the concept of regular locally connectedness and regular locally compactness on a topological space using the RL-closed sets.