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.
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.