@article { Gutman19950131,
  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."
}