Standard

Locally convex spaces with all Archimedean cones closed. / Гутман, Александр Ефимович; Емельяненков, Иван Александрович.

In: Siberian Mathematical Journal, Vol. 64, No. 5, 09.2023, p. 1117-1136.

Research output: Contribution to journal › Article › peer-review

Harvard

Гутман, АЕ & Емельяненков, ИА 2023, 'Locally convex spaces with all Archimedean cones closed', Siberian Mathematical Journal, vol. 64, no. 5, pp. 1117-1136. https://doi.org/10.1134/S0037446623050051

APA

Гутман, А. Е., & Емельяненков, И. А. (2023). Locally convex spaces with all Archimedean cones closed. Siberian Mathematical Journal, 64(5), 1117-1136. https://doi.org/10.1134/S0037446623050051

Vancouver

Гутман АЕ, Емельяненков ИА. Locally convex spaces with all Archimedean cones closed. Siberian Mathematical Journal. 2023 Sept;64(5):1117-1136. doi: 10.1134/S0037446623050051

Author

Гутман, Александр Ефимович ; Емельяненков, Иван Александрович. / Locally convex spaces with all Archimedean cones closed. In: Siberian Mathematical Journal. 2023 ; Vol. 64, No. 5. pp. 1117-1136.

BibTeX

@article{92e07a6e40554e6b9c3ed7cb3b47821b,
title = "Locally convex spaces with all Archimedean cones closed",
abstract = "We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of quasidense set and prove that the above class consists of all finite-dimensional and countable-dimensional spaces X whose topological dual X' is quasidense in the algebraic dual X# of X.",
keywords = "Archimedean ordered vector space, locally convex space, weak topology, cone, wedge, 517.98",
author = "Гутман, {Александр Ефимович} and Емельяненков, {Иван Александрович}",
note = "The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0004). Gutman A.E., Emelyanenkov I.A. Locally convex spaces with all Archimedean cones closed // Sib. Math. J. 2023. V. 64, N 5. P. 1117–1136.",
year = "2023",
month = sep,
doi = "10.1134/S0037446623050051",
language = "English",
volume = "64",
pages = "1117--1136",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "5",

}

RIS

TY - JOUR

T1 - Locally convex spaces with all Archimedean cones closed

AU - Гутман, Александр Ефимович

AU - Емельяненков, Иван Александрович

N1 - The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0004). Gutman A.E., Emelyanenkov I.A. Locally convex spaces with all Archimedean cones closed // Sib. Math. J. 2023. V. 64, N 5. P. 1117–1136.

PY - 2023/9

Y1 - 2023/9

N2 - We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of quasidense set and prove that the above class consists of all finite-dimensional and countable-dimensional spaces X whose topological dual X' is quasidense in the algebraic dual X# of X.

AB - We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of quasidense set and prove that the above class consists of all finite-dimensional and countable-dimensional spaces X whose topological dual X' is quasidense in the algebraic dual X# of X.

KW - Archimedean ordered vector space

KW - locally convex space

KW - weak topology

KW - cone

KW - wedge

KW - 517.98

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85172335601&origin=inward&txGid=29c0a7f7095881207d4e1617fb2d4eec

UR - https://www.mendeley.com/catalogue/b35eb78e-2c41-3c59-9c3c-8ef5b1339360/

U2 - 10.1134/S0037446623050051

DO - 10.1134/S0037446623050051

M3 - Article

VL - 64

SP - 1117

EP - 1136

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -

ID: 59189251