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This article is cited in 1 scientific paper (total in 2 paper)
On spaces in which the norm convergence coincides with the order convergence
B. Z. Vulikha, O. S. Korsakovab a 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.
Received: 26.01.1972
Citation:
B. Z. Vulikh, O. S. Korsakova, “On spaces in which the norm convergence coincides with the order convergence”, Mat. Zametki, 13:2 (1973), 259–268; Math. Notes, 13:2 (1973), 158–163
Linking options:
https://www.mathnet.ru/eng/mzm7119 https://www.mathnet.ru/eng/mzm/v13/i2/p259
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Abstract page: | 311 | Full-text PDF : | 144 | First page: | 2 |
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