CAJ | 학술논문

纤维拓扑与超空间拓扑，无论在理论上还是在应用中都是有意义的拓扑结构，两个研究领域都产生了丰富的成果。但是迄今为止，探讨复合两种结构的工作还基本没有出现。引入纤维超空间概念，并讨论纤维投射的基本性质。根据该复合结构的特点，定义了纤维超空间的局部紧以及纤维超空间具有局部紧纤维的概念，并讨论了两者间的关系，以及与基底空间相关性质的联系。得到了某些关于紧子集超空间和闭子集超空间纤维紧性，以及纤维超空间局部紧性的一些等价刻画。
섬유탁복여초공간탁복，무론재이론상환시재응용중도시유의의적탁복결구，량개연구영역도산생료봉부적성과。단시흘금위지，탐토복합량충결구적공작환기본몰유출현。인입섬유초공간개념，병토론섬유투사적기본성질。근거해복합결구적특점，정의료섬유초공간적국부긴이급섬유초공간구유국부긴섬유적개념，병토론료량자간적관계，이급여기저공간상관성질적련계。득도료모사관우긴자집초공간화폐자집초공간섬유긴성，이급섬유초공간국부긴성적일사등개각화。
Fibrewise topology and superspace topology are two meaningful topological structures both in theory and application ,and there are rich research achievements in both fields .So far ,however , there is little research work to compound the two structures .The paper poses the nation of fibrewise superspace ,and discusses the basic properties of fibrewise function .It also defines the local compact-ness of fibrewise superspace and the fibrewise superspace with local compact fibre ,and discusses the relations between the two properties .The equivalence conditions for fiberwise compactness of super-space of compact subsets and superspace of colsed subsets ,and the equivalent conditions of local compactness of fibrewise superspace are obtained in this paper .