The Open Limit Point Compactness

In this paper, we gave a new topological concept and we called it the open limit point compactness.We have proved that each of the compactness, and the limit point compactness is stronger than of the open limit point compactness., that is, compactness implies open limit point compactness, also limit point compactness implies open limit point compactness, but the converse is not true. Also we have shown that the continuous image of an open limit point compact is an open limit point compact and so this property is a topological property .This property is not a hereditary property. Connected spaces are open limit point spaces. The one-point compactification of a space is an open limit point compact. Finally, we have shown that if is an open limit point compact, then each of , and is an open limit point compact.