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Cross sections and homeomorphism classes of Abelian groups equipped with the Bohr topology by W.W. Comfort; Salvador Hernández; F. Javier Trigos-Arrieta is a Mathematics article available to read on EtoBox.

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A closed subgroup H of a topological group G is a ccs-subgroup if there is a continuous cross section from The symbol G # denotes an Abelian group G with its Bohr topology, i.e., the topology induced by Hom(G, T). A topological group H is an absolute ccs-group(#) (respectively, an absolute retract(#)) if H is a ccs-subgroup (respectively, is a retract) in every group of the form G # containing H as a (necessarily closed) subgroup. One then writes H ∈ ACCS(#) (respectively, H ∈ AR(#)). ## Theorem 1. Every ccs-subgroup H of a group of the form G a) Every cyclic group is in ACCS(#). (b) The classes ACCS(#) and AR(#) are closed under finite products. (c) Not every Abelian group is in ACCS(#). The following corollary to Theorem 3 answers a question of Kunen: Corollary. The spaces (div(Z)) # and ((div(Z)/Z) × Z) # are homeomorphic.

Who reads Cross sections and homeomorphism classes of Abelian groups equipped with the Bohr topology?

Author

W.W. Comfort; Salvador Hernández; F. Javier Trigos-Arrieta

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-8641)

Published

2001

Language

EN

Field

Mathematics (Physical Sciences)