Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 337-348
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R. K. Vasil'ev. The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes. Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 337-348. http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a14/
@article{MZM_1972_12_3_a14,
author = {R. K. Vasil'ev},
title = {The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes},
journal = {Matemati\v{c}eskie zametki},
pages = {337--348},
year = {1972},
volume = {12},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a14/}
}
TY - JOUR
AU - R. K. Vasil'ev
TI - The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes
JO - Matematičeskie zametki
PY - 1972
SP - 337
EP - 348
VL - 12
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a14/
LA - ru
ID - MZM_1972_12_3_a14
ER -
%0 Journal Article
%A R. K. Vasil'ev
%T The conditions for the convergence of isotonic operators in partially ordered sets with convergence classes
%J Matematičeskie zametki
%D 1972
%P 337-348
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a14/
%G ru
%F MZM_1972_12_3_a14
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 $x$.
