This article is cited in 1 paper

On spaces in which the norm convergence coincides with the order convergence

B. Z. Vulikh^a, O. S. Korsakova<sup>b

a</sup> A. A. Zhdanov Leningrad State University
^b A. I. Hertsen Leningrad State Pedagogical Institute

Abstract: We investigate partially ordered normed vector spaces in which the norm convergence coincides with the order convergence. We consider spaces where the convergences coincide for arbitrary nets and spaces where the convergences coincide only for sequences. We give conditions which characterize such spaces and investigate their properties. In particular, we study the problem of their Dedekind completeness and $\sigma$-completeness.

UDC: 513.88

Received: 26.01.1972

 English version: Mathematical Notes, 1973, 13:2, 158–163

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