T_2- Splitting points in Topological Spaces

Abstract

In this paper, we introduced a new splitting for points in topological spaces called it an lpT2 - space space using the concept of the derived set d(A) of a set A. We proved that this property is both a hereditary property and a topological property. The continuous image of an lpT2 - space needs not be an lpT2 - space. Also, we proved that the product space XxY is an lpT2 - space iff each of X and Y is an lpT2 - space. We proved that every classical lpT2 - space  is a completely ideal Hausdorff space.