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邻域套基与A_1公理

THE LOCALLY NESTED BASIS AND THE A_1 AXIOM
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摘要 该文给出一个无邻域套基的空间的例子,证明了在可分空间或拓扑向量空间中,邻域套基的存在性等价于A_1公理,并利用序数理论构造了一个非可分空间的例子,其中每点存在邻域套基但不满足A_1公理。 In this paper,an example of the space which has no locally nested basis of neigh-borhood has been given. In separable topological spaces or topological vector spaces ,the ex-istence of locally nested basis of neighborhood is equal with A_1 axiom A inseparable spacewhich has locally nested basis of neighborhood for each point of it but not obeyed with A_1 ax-iom has also been constructed.
作者 王见勇
出处 《宁夏大学学报(自然科学版)》 CAS 1995年第1期70-73,共4页 Journal of Ningxia University(Natural Science Edition)
关键词 领域套基 A1公理 良序 序数 拓扑空间 locally nested basis of neighborhood well ordering A_1 axiom ordinal numbers.
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