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Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 432–435 (Mi semr599)  

Real, complex and functional analysis

On upper topological limit of family of vector subspaces of codimension $k$

K. V. Storozhukab

a Novosibirsk State University, Pirogova str., 2, 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: Let $\{L_\alpha\mid \alpha\in I\}$ be an infinite family of subspaces in a topological vector space $X$ the codimension of each of which is at most $k$. We prove that there exists a subspace $L\subset X$, $\operatorname{codim} L\leq k$, such that every $x\in L$ is a limit point of some family $\{l_\alpha\in L_\alpha\}$.

Keywords: upper topological limit.

DOI: https://doi.org/10.17377/semi.2015.12.036

Full text: PDF file (130 kB)
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Document Type: Article
UDC: 517.982.2
MSC: 46A15
Received July 5, 2015, published July 20, 2015

Citation: K. V. Storozhuk, “On upper topological limit of family of vector subspaces of codimension $k$”, Sib. Èlektron. Mat. Izv., 12 (2015), 432–435

Citation in format AMSBIB
\Bibitem{Sto15}
\by K.~V.~Storozhuk
\paper On upper topological limit of family of vector subspaces of codimension~$k$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 432--435
\mathnet{http://mi.mathnet.ru/semr599}
\crossref{https://doi.org/10.17377/semi.2015.12.036}


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