Group Structures and Rectifiability in Powers of Spaces

Tom 55 / 2007

G. J. Ridderbos Bulletin Polish Acad. Sci. Math. 55 (2007), 357-363 MSC: 54A25, 54B10, 54H11. DOI: 10.4064/ba55-4-7


We prove that if some power of a space $X$ is rectifiable, then $X^{\pi w(X)}$ is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangel'skiĭ. We also show that in Mal'tsev spaces of point-countable type, character and $\pi$-character coincide.


  • G. J. RidderbosFaculty of Sciences
    Division of Mathematics
    Vrije Universiteit
    De Boelelaan 1081 A
    1081 HV Amsterdam, the Netherlands

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