论文标题
有限的统一的均匀封闭的司法化
Uniformly closed sublattices of finite codimension
论文作者
论文摘要
该论文研究了阿基米德矢量晶格中均匀封闭的子空间，sublattices和有限编码的理想。结果表明，有限编码的每个均匀封闭的子空间（或sublattice）都可以写成Codimension One的均匀封闭子空间（分别是Sublattices）的相交。每个统一的封闭的sublattice of Codimension $ n $都包含一个统一的封闭的codimension理想，最多$ 2N $。如果矢量晶格均匀地完成，则有限的编辑的每个理想都均匀地关闭。该论文的结果扩展了[AL90A，AL90B]的结果（并动机），以及Kakutani对$ C（k）$空间的封闭sublattices的表征。
The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection of uniformly closed subspaces (respectively, sublattices) of codimension one. Every uniformly closed sublattice of codimension $n$ contains a uniformly closed ideal of codimension at most $2n$. If the vector lattice is uniformly complete then every ideal of finite codimension is uniformly closed. Results of the paper extend (and are motivated by) results of [AL90a,AL90b] and , as well as Kakutani's characterization of closed sublattices of $C(K)$ spaces.
