论文标题
投影带的表征和连续函数晶格的某些顺序特性
Characterizations of the projection bands and some order properties of the lattices of continuous functions
论文作者
论文摘要
我们表明，对于Archimedean Vector晶格$ f $的理想$ H $，以下条件等效： $ \ bullet $ $ h $是投影频段； $ \ bullet $ $ h $中的任何相互不相交的矢量集合以$ f $为界的订单，均以$ h $为界的订单； $ \ bullet $ $ h $是晶格$ \ Mathcal {i} _ {f} $ $ f $中所有理想的无限见面元素。 $ \ MATHCAL {J} \ subset \ Mathcal {i} _ {f} $。 此外，我们表明，如果$ f $均匀地完成，而$ h $是统一关闭的主体理想，那么$ h $是投影带。在此过程中，我们研究了Tychonoff拓扑空间上连续功能的晶格的一些顺序特性。
We show that for an ideal $H$ in an Archimedean vector lattice $F$ the following conditions are equivalent: $\bullet$ $H$ is a projection band; $\bullet$ Any collection of mutually disjoint vectors in $H$, which is order bounded in $F$, is order bounded in $H$; $\bullet$ $H$ is an infinite meet-distributive element of the lattice $\mathcal{I}_{F}$ of all ideals in $F$ in the sense that $\bigcap\limits_{J\in \mathcal{J}}\left(H+ J\right)=H+ \bigcap \mathcal{J}$, for any $\mathcal{J}\subset \mathcal{I}_{F}$. Additionally, we show that if $F$ is uniformly complete and $H$ is a uniformly closed principal ideal, then $H$ is a projection band. In the process we investigate some order properties of lattices of continuous functions on Tychonoff topological spaces.
