S －次仿紧空间

针对一些广义仿紧空间以及拓扑空间中半开集和半闭集的性质，本文将次仿紧空间的一些结论推广到半闭集的条件下，新定义并研究S －次仿紧空间的基本性质。首先给出一些基本的定义和定理，然后在此基础上定义S－次仿紧空间，最后得出一些主要结果：（1）空间X是S－次仿紧空间，则X的每一开覆盖U，存在半开加细覆盖序列｛Vn｝n∈N使对每一x∈X，存在n∈N，使ord（x，Vn）＝1，这里（ord（x，Vn）＝｜｛V：V∈Vn，x∈V｝｜）；（2）空间X是S－次仿紧空间，则X的每一开覆盖具有σ垫状加细覆盖；（3）如果（X，Fa）是S－次仿紧空间，则（X，F）也是S－次仿紧空间，并给出相应的证明。

S-subparacompact Spaces

Based on a series of generalized paracompact spaces and the properties of semi -open and semi-closed sets in topological spaces , some conclusions of sub -paracompact spaces were spread to semi -closed sets.The definition of S -subparacomact space was given and its basic properties was studied .Some basic defi-nitions and theorems in topological spaces were given first , and then the definition of S -subparacompact space was introduced .Some main results were obtained as follows： （ 1 ） Let X be a S-subparacompact space , then each open cover U of X has a semi-open n∈N refinements{Vn}n∈N and for every x∈X , there exists a positive integrity such that only belongs to one set of Vn ,i.e.ord（ x,Vn ） =1 .（2） If X is a S-subparacompact space . Then each open cover U of X has a refinement which isσ-cushioned in the family U .（3） Suppose （X,Tα） is a S-subparacompact space.Then the space （X,T） is S-subparacompact.At same time, their corresponding proofs are presented .