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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1553–1555 (Mi semr1013)  

Real, complex and functional analysis

Subtle hyperplanes

K. V. Storozhukab

a Sobolev Institute of Mathematics, 4, pr. Koptyuga, Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: We show that the countably-dimensional vector space $C_{00}$ of all sequences with finite support contains a convex cone $K$ that does not include straight lines and is closed Archiemedean but not closed in the Mackey topology $\tau$ corresponding to the duality $\langle C_{00}| F\rangle$, where $F$ is a hyperplane in the algebraic dual space $C_{00}^#$.

Keywords: cone, duality of topology vector spaces.

DOI: https://doi.org/10.33048/semi.2018.15.128

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Bibliographic databases:

UDC: 517.982
MSC: 46A03, 52A07
Received September 20, 2018, published December 4, 2018

Citation: K. V. Storozhuk, “Subtle hyperplanes”, Sib. Èlektron. Mat. Izv., 15 (2018), 1553–1555

Citation in format AMSBIB
\Bibitem{Sto18}
\by K.~V.~Storozhuk
\paper Subtle hyperplanes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1553--1555
\mathnet{http://mi.mathnet.ru/semr1013}
\crossref{https://doi.org/10.33048/semi.2018.15.128}


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