Group topologies making every continuous homomorphic image to a compact group connected

Yanez Victor Hugo

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Group topologies making every continuous homomorphic image to a compact group connected

机译：Group topologies making every continuous homomorphic image to a compact group connected

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A topological group is minimally almost periodic (MinAP) if the only continuous homomorphism to any compact group is trivial. Dikranjan and Shakhmatov proved that if an abelian group can be equipped with a MinAPgroup topology, then for every m is an element of N the subgroup mG of G is either the trivial group or has infinite cardinality. In this paper we prove the following: if an abelian group Gcan be equipped with a group topology making all of its continuous homomorphic images to a compact group connected, then it admits a MinAPgroup topology. This condition becomes sufficient as well, as every MinAP topological group only has trivial continuous homomorphic images in compact groups. (C) 2021 Elsevier B.V. All rights reserved.

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《Topology and its applications》 |2022年第15期|107958.1-107958.12|共12页
作者
Yanez Victor Hugo;
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Nanjing Normal Univ, Inst Math, Nanjing 210046, Peoples R China;

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正文语种英语
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Minimally almost periodic group; Maximally almost periodic group von Neumann kernel; Bohr topology; Bohr compactification; Connected group; Pathwise connected group; Continuous homomorphic image;

Group topologies making every continuous homomorphic image to a compact group connected

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