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Vendeur : Leopolis, Kraków, PologneLeopolis
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Soft cover. Etat : New. 1st Edition. 8vo (21.5 cm), 112 pp. Publisher's laminated wrappers. Mathematical Studies: Monograph Series, vol. 4. A research monograph in topological algebra devoted to the systematic development of the theory of T-sequences, a notion introduced by the authors in their earlier work. A sequence ⟨an⟩ in a… group G is a T-sequence if there exists a Hausdorff group topology on G in which the sequence converges to the identity; every T-sequence determines a maximal group topology in which it converges, called the topology determined by that sequence. The authors develop this as a constructive method for producing group topologies with prescribed topological-algebraic properties by varying the arithmetic properties of the underlying sequence. Among the results obtained by this approach are solutions to several open problems in the theory of topological groups, including the existence of complete sequential group topologies of sequential order ω1 on countable topologizable groups, complete group topologies on infinite Abelian groups whose characters do not separate points, and, under CH, nondiscrete group topologies on infinite Abelian groups in which all closed subsets are nowhere dense. Further applications include the topological classification of countable kω-groups, characterization of minimal varieties of topological groups and complementable group topologies on Abelian groups, and simplified proofs of the Markov criterion for topologizability of countable groups and Arnautov's theorem on the topologizability of countable rings. The five chapters cover filters and topological groups and rings; T-sequences in Abelian groups, including T-filters, sequentiality, completeness, complementability, refinements, and characters; T-sequences in countable groups and rings; topologies determined by compact subsets, including kω-spaces and kω-groups; and discrete subsets and expansive sequences. An important specialized contribution to modern topological algebra, particularly valuable for the study of sequential convergence, group topologies, and constructive methods in infinite algebraic structures.
