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Mat. Zametki, 1972, Volume 12, Issue 3, Pages 337–348 (Mi mz9886)  

The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes

R. K. Vasil'ev

Moscow Institute of Highways

Abstract: The necessary and sufficient conditions are given which must be satisfied by an element $x$ of a partially ordered set $X$ with convergence close to topological in order that every net of isotonic operators of the set $X'\subset X$ in $X$, converging on some set $G\subset X'$ to the identity operator, should converge on $X$ to $x$.

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English version:
Mathematical Notes, 1972, 12:3, 632–637

Bibliographic databases:

UDC: 513.88
Received: 23.08.1971

Citation: R. K. Vasil'ev, “The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes”, Mat. Zametki, 12:3 (1972), 337–348; Math. Notes, 12:3 (1972), 632–637

Citation in format AMSBIB
\Bibitem{Vas72}
\by R.~K.~Vasil'ev
\paper The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 3
\pages 337--348
\mathnet{http://mi.mathnet.ru/mz9886}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=374989}
\zmath{https://zbmath.org/?q=an:0244.47027}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 3
\pages 632--637
\crossref{https://doi.org/10.1007/BF01094000}


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