Self-duality in the class of precompact groups |
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| Authors: | Mikhail Tkachenko |
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| Institution: | Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C.P. 09340, México, D.F., Mexico Departament de Matemàtiques, Universitat Jaume I, Campus del Riu Sec, Castelló de la Plana, E-12071, Spain |
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| Abstract: | A topological Abelian group G is called (strongly) self-dual if there exists a topological isomorphism Φ:G→G∧ of G onto the dual group G∧ (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 κω=κ, there exists a pseudocompact, non-compact, strongly self-dual Boolean group of cardinality κ. |
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| Keywords: | primary 43A40 22A05 54H11 secondary 54D30 54G20 |
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