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Gutman A.E.
Locally one-dimensional complete vector lattices //
Doklady Math. 1997. V. 55, N 2. P. 240–241.

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^=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 σ-distributive.
Type Article
Authors Gutman Alexander Efimovich
Title Locally one-dimensional complete vector lattices
Journal Doklady Mathematics
Year 1997
Volume 55
Number 2
Pages 240–241
Language English
© 1995.01.31
Links
Project  The Wickstead problem 
Description of the vector lattices E for which all band-preserving operators TE → E are regular
 
 
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July 19, 2018