Some Properties Of The Relative Topological Space And The Weak J-space

Based on the existent knowledge, some properties of the relative topological space and the weak J -space are summarized and generalized in this thesis. And some new results are proved.I. It is proved that if X is a Hausdorff space, Y is paracompact in X , then Y is regular in X . The relative topological properties of subspace of regular, normal, compact, paracompact and sequential space under maps and other separation properties are also discussed. And some known results are generalized.II.It is proved that the weak J-space has many properties which are very similar to J-space, that is, let {X1,X2,K} beclosed cover of X with K compact and Xlr^X2=Q>, then X is a weak J -space if and only if Xl and X2 are weak J-spaces, and X1 or X2 is compact. And if X} and X2 are connected weak J -space, then Xl x X^ is connected weak J -space and so on. At last, the cone of J -space is discussed. Some new properties are obtained.