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Fundamentalnaya i Prikladnaya Matematika, 2003, Volume 9, Issue 1, Pages 3–18
(Mi fpm708)
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On disjoint sums in the lattice of linear topologies
V. I. Arnautov, K. M. Filippov Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
Abstract:
Let $M$ be a vector space over a skew-field equipped with the discrete topology, $\mathcal L(M)$ be the lattice of all linear topologies on $M$ ordered by inclusion, and $\tau_*,\tau_0,\tau_1\in\mathcal L(M)$. We write $\tau_1=\tau_*\sqcup\tau_0$ or say that $\tau_1$ is a disjoint sum of $\tau_*$ and $\tau_0$ if $\tau_1=\inf\{\tau_0,\tau_*\}$ and $\sup\{\tau_0,\tau_*\}$ is the discrete topology. Given $\tau_1,\tau_0\in\mathcal L(M)$, we say that $\tau_0$ is a disjoint summand of $\tau_1$ if $\tau_1=\tau_*\sqcup\tau_0$ for a certain $\tau_*\in\mathcal L(M)$. Some necessary and some sufficient conditions are proved for $\tau_0$ to be a disjoint summand of $\tau_1$.
Citation:
V. I. Arnautov, K. M. Filippov, “On disjoint sums in the lattice of linear topologies”, Fundam. Prikl. Mat., 9:1 (2003), 3–18; J. Math. Sci., 128:6 (2005), 3335–3344
Linking options:
https://www.mathnet.ru/eng/fpm708 https://www.mathnet.ru/eng/fpm/v9/i1/p3
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Abstract page: | 250 | Full-text PDF : | 102 | References: | 40 | First page: | 2 |
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