@article { Gutman19941102,
  author = "Gutman A.E.",
  title = "Locally one-dimensional K-spaces and $\sigma$-distributive Boolean algebras",
  journal = "Siberian Adv. Math.",
  year = "1995",
  volume = "5",
  number = "1",
  pages = "42--48",
  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.",
  keywords = "locally one-dimensional K-space, discrete K-space, $\sigma$-distributive Boolean algebra, $\sigma$-inductive Boolean algebra, atomic Boolean algebra, regular operator, real numbers in a Boolean-valued universe"
}
@inproceedings { Gutman19940725,
  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."
}
@article { Gutman19950130,
  author = "Gutman A.E.",
  title = "Locally one-dimensional K-spaces",
  journal = "Proc. Acad. Sci.",
  year = "1997",
  volume = "353",
  number = "5",
  pages = "590--591",
  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."
}
@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."
}
@booklet { Gutman20071210,
  author = "Gutman A.E. and Kusraev A.G. and Kutateladze S.S.",
  note = "Preprint / IAMI VSC RAS; N 3",
  title = "The Wickstead problem",
  address = "Vladikavkaz",
  year = "2007",
  pages = "44",
  doi = "10.13140/RG.2.2.22573.79849",
  annote = "In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.",
  keywords = "band preserving operator, universally complete vector lattice, $\sigma$-distributive Boolean algebra, local Hamel basis, transcendence basis, derivation, Boolean valued representation"
}
@booklet { Gutman20071214,
  author = "Gutman A.E. and Kusraev A.G. and Kutateladze S.S.",
  note = "Electronic preprint / arXiv:0712.2378 [math.FA]",
  howpublished = "Electronic",
  title = "The Wickstead problem",
  address = "arXiv.org",
  year = "2007",
  pages = "44",
  annote = "In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.",
  keywords = "band preserving operator, universally complete vector lattice, $\sigma$-distributive Boolean algebra, local Hamel basis, transcendence basis, derivation, Boolean valued representation"
}
@article { Gutman20080213,
  author = "Gutman A.E. and Kusraev A.G. and Kutateladze S.S.",
  howpublished = "Electronic",
  title = "The Wickstead problem",
  journal = "Sib. Electron. Math. Rep.",
  year = "2008",
  volume = "5",
  pages = "293--333",
  annote = "In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.",
  keywords = "band preserving operator, universally complete vector lattice, $\sigma$-distributive Boolean algebra, local Hamel basis, transcendence basis, derivation, Boolean valued representation"
}