Group Structures and Rectifiability in Powers of Spaces
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 357-363
MSC: 54A25, 54B10, 54H11.
DOI: 10.4064/ba55-4-7
Abstract
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.
