Order convergence in infinite-dimensional vector lattices is not topological

Autor:	Dabboorasad, Y. A., Emelyanov, E. Y., Marabeh, M. A. A.
Rok vydání:	2017
Předmět:	Mathematics - Functional Analysis 46A16 46A40 46B30
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1705.09883 Zobrazit plný text záznamu View this record from Arxiv