Some Properties Of The Relative Topology

This thesis mainly discusses the following properties of the relative topology:I. Some relative topological properties on sum space, such as relative strongly normality, relative normality, relative internally normality, relative compact, relative paracompact (1-paracompact) and relative countable compact. The main conclusion is following: Ys is subspace of space^ for each s S,and YS have one ofthe above relative property in ?Xs if and only if Ys have thisproperty in Xs for each s S.II. Some relative properties under mappings. We consider the following relative properties under the perfect map, the quasi-perfect map or the close Lindelof map: relative countable 1-paracompact, relative 1-paracompact, relative countable compact, relative nearly paracompact and relative Lindelof.III. We define two classes of relative space: 7 is nearly paracompact hi X and 7 is nearly weak paracompact in X. We also discuss the relation between them and the relation of these two spaces to other relative spaces, such as relative compact, relative paracompact, relative nearly paracompact and relative weak paracompact. At last, we get a sufficiency and necessary condition of relative superregular.