THE Set of Complete Cluster Point and (?)α-Compactness

Abstract:

      In this paper we introduce the concept for the set of complete cluster point and (?)_α-cormpactness in the metric space. We have proved several primitive properties relatedto the complete cluster point and set of complete cluster point. We have discussed the relationship among some kinds of (?)_α-compactness; and analysed the relationship among the (?)_α-compactness and the general compactness. We have found that the (?)_α-compactness and the general compactness are eqivalent to each other in the metric space.