author = "Gutman A.E.",

title = "Locally one-dimensional complete vector lattices",

journal = "Doklady Math.",

year = "1997",

volume = "55",

number = "2",

pages = "240--241",

annote = "It is known that all band preserving operators acting in a universally complete K-space are regular if and only if the K-space is locally one-dimensional. In addition, a K-space with base $B$ is locally one-dimensional if and only if $R^{\land}=R$ in $V^{(B)}$. It seems to have been unknown so far whether there exist nondiscrete locally one-dimensional K-spaces. In the present note we give a positive answer to the question. As an auxiliary result, we establish that a K-space is locally one-dimensional if and only if its base is $\sigma$-distributive."