1) Locally-countable bases
局部-可数基
2) countable local base
可数局部基
3) locally countable
局部可数
4) locally countable compact
局部可数紧
1.
We give some concepts of different locally countable compact space and locally countable paracompact space,discuss their natures,and give some results as every closed subset in countable paracompact space is countable paracompact )If topological space is a neighborhood open locally countable paracompact space, is any open set of,then is a neighborhood open locally countable paracompact subspace.
文章给出了几种类型局部可数紧空间和几种类型局部可数仿紧空间的概念,讨论了它们的一些性质,给出可数仿紧空间的每一闭子集都是可数仿紧的;若拓扑空间X是邻域开包局部可数仿紧空间,A是X中任一开集,则A是邻域开包局部可数仿紧子空间等一些有益的结果。
5) locally countable family
局部可数族
6) σ-locally countable
σ-局部可数
1.
Two main theorems are proved:(1) Topological space X has a σ-locally countable base if X is a q-space with a σ-locally countable k-network;(2) Let Xn (n∈N) have a σ-locally countable k-network.
证明了下列两个定理：（１）Ｘ有σ－局部可数基的充分必要条件是Ｘ是ｑ－空间且有－σ－局部可数ｋ－网。
补充资料：局部维数
局部维数
local dimension
局部维数【l仪川由m“‘叨;加~研二pa3Mepooc、]，正规拓扑空间X的 拓扑不变量fo。山mX，定义如下二』仪山mX《n，n一一1，O，1，，·，如果任何一点x任X都有一个邻域O二，使得其闭包的h加卿此维数(玩比gued而-enslon)满足关系d如J*(n.如果对某个n有1o。djmX簇n，那么X的局部维数是有限的，记为loc-山mX<+的，定义 l以刀imX=~{。:l以沮imX簇时·kiul血nX簇dimX恒成立;的确存在正规空间X使得locdjn1X
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