Some Properties Of Relative Topology

This thesis is divided into three chapters.In Chapter 1, we introduce basic notions and major theorems of general topology, and present a brief history of topology, we also made a detailed de-scription of symbols which be used in the article.In Chapter 2, we introduce the historical background of relative topology, and describes some concepts and theorems of relative topology.In Chapter 3, we define some concepts as follow:Y is locally compact in X and X is regular on Y. Discuss under what condition that X is superregular on Y. We also make a preliminary describe the relation between X is regular on Y and X is normal on Y. Finally, the main conclusions of the paper and detailed proof the main conclusions are as follows:Let Y be a subspace of a space X. First, if Y is open in X and Y is paracompact in X, then Y is 1 paracompact in X. Second, if X is the union of Y and Z, and Y,Z are 1-paracompact in X, then X is paracompact space. Third, if Y is superregular in X and Y is Lindelof space, then Y is paracompact in X. Fourth, if X is Hausdorff space,Y is local compact inX, then Y is superregular in X. Fifth, if X is Lindelof space, and X is regular on Y, then X is normal on Y. Sixth, if X is paracompact, and X is regular on Y, then X is normal on Y.