无界order convergence上的一些松散末端
Some loose ends on unbounded order convergence
摘要：
将几乎处处收敛的概念推广到向量格上，得到了无界阶收敛的结果，这在向量格和巴拿赫格理论中是一个非常有用的工具.在这个简短的说明中，我们建立了一些新的结果，无界的顺序收敛，捆绑一些松散的结束。特别地，我们证明了序连续巴拿赫格中的每个范数有界正增网都是uo-Cauchy网，序连续巴拿赫格中的每个uo-Cauchy网在泛完备下都有uo-极限.
英文摘要：
The notion of almost everywhere convergence has been generalized to vector lattices as unbounded order convergence, which proves a very useful tool in the theory of vector and Banach lattices. In this short note, we establish some new results on unbounded order convergence that tie up some loose ends. In particular, we show that every norm bounded positive increasing net in an order continuous Banach lattice is uo-Cauchy and that every uo-Cauchy net in an order continuous Banach lattice has a uo-limit in the universal completion.
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