Generalized α-closed maps and α-generalized closed maps

Njastad(1) and Levine(2), respectively, have introduced the notion of alpha-sets and generalized closed sets. Recently, the concept of generalized alpha-closed sets(3) and alpha-generalized closed sets(4) have been introduced as generalizations of alpha-closed sets and generalized closed sets respectively. in this paper, the authors introduce and investigate the concept of generalized alpha-closed maps, alpha-generalized closed maps and alpha-regular spaces as generalization of closed maps, generalized closed maps and regular spaces respectively. By introducing the concept of pre-alpha-closed maps, it is proved that normality and alpha-regularity are preserved under the maps.