非Hausdorff线性拓扑空间的拓扑结构

THE TOPOLOGICAL STRUCTURE OF NON-HAUSDORFF LINEAR TOPOLOGICAL SPACE

通过引入丛集、带集、带空间等概念，证明了任何非Ｈａｕｓｄｏｒｆｆ线性拓扑空间都是带空间，其拓扑结构由零，或集的闭包（子空间）决定，是具有固定形式的．随后作为特例，讨论了有限维非Ｈａｕｓｄｏｒｆｆ空间，给出了更强的结果。

By introducing the definition of bundle-set, strip-set and strip-space,this paper provesthat every non-Hausdorff linear topological space is a strip-space, Moreover , its structure oftopology can be determined by the closure of subspace{θ}, namely,{θ}. Then the finite-di-mentional non-Hausdorff space is dealt with as a special example and further results are at-tained。