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arXiv · 1705.09883

Order convergence in infinite-dimensional vector lattices is not topological

Y. A. Dabboorasad·E. Y. Emelyanov·M. A. A. Marabeh
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Abstract

In this note, we show that the order convergence in a vector lattice $X$ is not topological unless $\dim X<\infty$. Furthermore, we show that, in atomic order continuous Banach lattices, the order convergence is topological on order intervals.

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Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh. 2017-05-28. Order convergence in infinite-dimensional vector lattices is not topological. https://arxiv.org/abs/1705.09883

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