CAJ | 학술논문

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。
침대일사엄의방긴공간이급탁복공간중반개집화반폐집적성질，본문장차방긴공간적일사결론추엄도반폐집적조건하，신정의병연구S －차방긴공간적기본성질。수선급출일사기본적정의화정리，연후재차기출상정의S－차방긴공간，최후득출일사주요결과：（1）공간X시S－차방긴공간，칙X적매일개복개U，존재반개가세복개서렬｛Vn｝n∈N사대매일x∈X，존재n∈N，사ord（x，Vn）＝1，저리（ord（x，Vn）＝｜｛V：V∈Vn，x∈V｝｜）；（2）공간X시S－차방긴공간，칙X적매일개복개구유σ점상가세복개；（3）여과（X，Fa）시S－차방긴공간，칙（X，F）야시S－차방긴공간，병급출상응적증명。
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 .