On Topologies on the Group (\Z_p)^\N

2016/09/30 by Ivan Babenko, Babenko, I. K., Семеон Антонович Богатый +1
Mathematics · #Advanced Topology and Set Theory #Advanced Banach Space Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1610.00046

Abstract

It is proved that, on any Abelian group of infinite cardinality \bf m, there exist precisely 2^2^{\bf m} nonequivalent bounded Hausdorff group topologies. Under the continuum hypothesis, the number of nonequivalent compact and locally compact Hausdorff group topologies on the group (\Z_p)^\N is determined.

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