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Mat. Zametki, 1968, Volume 3, Issue 3, Pages 279–284 (Mi mz6679)  

Regulator convergence in commutative $l$-groups

È. E. Gurevich

A. I. Hertsen Leningrad State Pedagogical Institute

Abstract: In the theory of lattice ordered groups there are considered several types of convergence. In this work it is shown that for nets ($r$)-convergence is essentially stronger than ($o$)-convergence, while for sequences these notions are not comparable (as is known, in $K$-lineals, ($r$)-convergence for sequences as well as for nets is stronger than ($o$)-convergence); in $K_\sigma$-groups ($r$)-convergence of sequences is stronger than ($o$)-convergence. (A sequence is considered ($o$)-convergent if it is compressed by monotone sequences to a common limit.)

Full text: PDF file (417 kB)

English version:
Mathematical Notes, 1968, 3:3, 178–181

Bibliographic databases:

UDC: 512.4
Received: 03.04.1967

Citation: È. E. Gurevich, “Regulator convergence in commutative $l$-groups”, Mat. Zametki, 3:3 (1968), 279–284; Math. Notes, 3:3 (1968), 178–181

Citation in format AMSBIB
\Bibitem{Gur68}
\by \`E.~E.~Gurevich
\paper Regulator convergence in commutative $l$-groups
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 3
\pages 279--284
\mathnet{http://mi.mathnet.ru/mz6679}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=228398}
\zmath{https://zbmath.org/?q=an:0174.31401}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 3
\pages 178--181
\crossref{https://doi.org/10.1007/BF01387330}


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