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This problem is presented as an open problem 1.31. on p.26 of Arhangel'skii-Tkachenko, Topological groups and related structures. Is this problem still open?

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  • $\begingroup$ My collegue posed this question to MathOverflow server, however it is still without any answer or comment. $\endgroup$ – mcihak Nov 26 '13 at 17:29
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As I already told you at the workshop, Taras Banakh and me solved this problem. But, surprisingly and converse to that I told at the workshop, the answer is affirmative. This is why is good to write a common paper: if one of the authors is trying to prove a conjecture and another is trying to refute it then one of them should be right. :-)

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Yes, this problem is still open for many years and seems to be very hard. If you need a reference for this, you can add it, for instance, as "[Rav] Alex Ravsky. A personal communication". :-)

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