2024-03-29T11:33:25Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/437282022-12-02T15:25:25Zcom_10234_7037com_10234_9col_10234_8635
00925njm 22002777a 4500
dc
Tkachenko, Mikhail
author
2009
A topological Abelian group G is called (strongly) self-dual if there exists a topological isomorphism Φ : G → G<sup>∧</sup> of G onto the dual group G<sup>∧</sup> (such that Φ (x) (y) = Φ (y) (x) for all x, y ∈ G). We prove that every countably compact self-dual Abelian group is finite. It turns out, however, that for every infinite cardinal κ with κ<sup>ω</sup> = κ, there exists a pseudocompact, non-compact, strongly self-dual Boolean group of cardinality κ. © 2009 Elsevier B.V. All rights reserved.
Topology and its Applications, 156, 12, p. 2158-2165
1668641
http://hdl.handle.net/10234/43728
http://dx.doi.org/10.1016/j.topol.2009.03.039
Countably compact
Countably pseudocompact
Dual group
MAP group
Precompact
Pseudocompact
Reflexive
Self-dual
Self-duality in the class of precompact groups