Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
About group topologies of the primary Abelian group.
Authors: Arnautov Vladimir
1. φ'(G2) = G2;
2. g − φ(g) ∈ G1 for any g ∈ G;
3. φ: (G, τ) → (G, &tau′) is a topological isomorphism.
– 0.13 Mb
Abstract
Let G be any Abelian group of the period pn and G1 = {g ∈ G|pg = 0}, G2 = {g ∈ G|pn−1g = 0}. If τ and τ′ are a metrizable, linear group topologies such that G2 is a closed subgroup in each of topological groups (G, τ) and (G, τ′), then τ|G2 = τ′|G2 and (G, &tau)/G1 = (G, τ′)/G1 if and only if there exists a group isomorphism φ: G → G such that the following conditions are true:1. φ'(G2) = G2;
2. g − φ(g) ∈ G1 for any g ∈ G;
3. φ: (G, τ) → (G, &tau′) is a topological isomorphism.
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Contents
- Optimal control for one complex dynamic system, II
- About group topologies of the primary Abelian group.
- A complete classification of quadratic differential systems according to the dimensions of Aff(2, R)-orbits
- On stability and quasi-stability radii for a vector combinatorial problem with a parametric optimality principle.
- On preradicals associated to principal functors of module categories, I.
- Dynamic Programming Algorithms for Solving Stochastic Discrete Control Problems.
- On a Generalization of Hardy-Hilbert's Integral Inequality.
- The cubic differential system with six real invariant straight lines along three directions.
- A note on a subclass of analytic functions defined by a differential operator.
