THE CLOSED LIMIT POINT COMPACTNESS

ABSTRACT

In this paper, we gave a new topological concept and we called it The closed limit point compactness. This concept is stronger than the concept of a limit point compactness, that is, every a closed limit point compact space is a limit point compact space but the converse is not true. We have proved that the property of being a closed limit point compact is a topological property but not a hereditary property but it inherits to the closed subspace. We have shown that the continuous image of a closed limit point compact need not be a closed limit point compact. Also, we have shown that the quotient space of a closed limit point compact need not be a closed limit point compact. Finally, we have shown that if  is a closed limit point compact and  is a  -space, then  is a closed limit point compact. 

FULL TEXT