Matematicheskie Zametki
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $x$.

Full text: PDF file (1700 kB)

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

Bibliographic databases:

UDC: 513.88

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}