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- W2997052660 abstract "A topological space is reversible if each continuous bijection of it onto itself is open. We introduce an analogue of this notion in the category of topological groups: A topological group G is g-reversible if every continuous automorphism of G (=continuous isomorphism of G onto itself) is open. The class of g-reversible groups contains Polish groups, locally compact σ-compact groups, minimal groups, abelian groups with the Bohr topology, and reversible topological groups. We prove that subgroups of Rn are g-reversible, for every positive integer n. An example of a compact (so reversible) metric abelian group having a countable dense non-g-reversible subgroup is given. We also highlight the differences between reversible spaces and g-reversible topological groups. Many open problems are scattered throughout the paper." @default.
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- W2997052660 date "2020-04-01" @default.
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- W2997052660 title "Topological groups all continuous automorphisms of which are open" @default.
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- W2997052660 doi "https://doi.org/10.1016/j.topol.2019.107051" @default.
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