author = "Gutman A.E.",

title = "Locally one-dimensional K-spaces and $\sigma$-distributive Boolean algebras",

booktitle = "Siberian Conference on Applied and Industrial Mathematics (Novosibirsk, July 25--29, 1994): Proceedings",

address = "Novosibirsk",

publisher = "IM SB RAS",

year = "1997",

volume = "1",

pages = "103--108",

language = "russian",

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."