λ-Generalizations And g- Generalizations

Abstract

In this paper, we use the concept of λ-closed set and g-closed set to define two classes of generalized regular closed sets; namely λ-generalizations and g-generalizations. The class of λ-generalizations includes: r λ-closed set, r^*λ-closed set and r〖 λ〗^*-closed set, while the second class of generalizations includes: g.r-closed set, g.r-closed set and r.g^*-closed set. We investigate the characterizations of these generalizations, moreover, we illustrate the implications of these classes among themselves and with the known sets, and finally we study their behavior in regular spaces and in extremely disconnected spaces