论文标题
Riesz空间上的完整晶格收敛
Full Lattice Convergence on Riesz Spaces
论文作者
论文摘要
局部固体Riesz空间上的完整晶格收敛是拓扑，顺序和相对均匀收敛的抽象。我们研究了Riesz空间上完整收敛$ \ MATHBB {C} $的四个修改。第一个产生顺序收敛$ \ mathbb {sc} $。第二个使绝对$ \ mathbb {c} $ - 收敛并概括了绝对弱收敛。第三个修改使无界的$ \ mathbb {c} $ - 收敛，并概括了最近在文献中研究的各种无界融合。每当$ \ mathbb {c} $是$ \ mathbb {c} $的乘法修改$ \ mathbb {mcrbb {mcrbb {c} $时，最后一个是适用的。我们研究完整晶格收敛的一般特性，重点是普遍完整的Riesz空间和Archimedean $ f $ -Elgebras。本文中的技术和结果统一并扩展了在最近的无限融合文献中开发和获得的技术。
The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence $\mathbb{c}$ on a Riesz space. The first one produces a sequential convergence $\mathbb{sc}$. The second makes an absolute $\mathbb{c}$-convergence and generalizes the absolute weak convergence. The third modification makes an unbounded $\mathbb{c}$-convergence and generalizes various unbounded convergences recently studied in the literature. The last one is applicable whenever $\mathbb{c}$ is a full convergence on a commutative $l$-algebra and produces the multiplicative modification $\mathbb{mc}$ of $\mathbb{c}$. We study general properties of full lattice convergence with emphasis on universally complete Riesz spaces and on Archimedean $f$-algebras. The technique and results in this paper unify and extend those which were developed and obtained in recent literature on unbounded convergences.
