arXiv · 0709.2893
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
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Liljana Babinkostova, Marion Scheepers. 2007-09-18. Selection principles and countable dimension. https://arxiv.org/abs/0709.2893
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We construct a connected (indeed, path-connected) Hausdorff topological group G such that, for an odd n >= 665, the identity x^n = e holds in some neighbourhood of the identity but does not hold in the whole group. This answers in the negative a question of Mycielski and Aronszajn (Question 2.48 of the Kourovka Notebook). The construction uses the Graev extension of metrics to free topological groups and results of Adian and Adian-Atabekyan (for n > 10^10, alternatively, of Ol'shanskii and Ashmanov-Ol'shanskii) on free Burnside groups and their central extensions.
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