A topological group is embeddble in a product of a family of second-countable topological groups if and only if it is $\omega$-narrow

Question

How to prove the following property: a topological group is topologically isomorphic to a subgroup of the product of some family of second-countable topological groups if and only if it is ω-narrow

You might want to include a definition of "$\omega$-narrow" and perhaps provide some reasoning why you think this result is true. (For example, if you have read it somewhere, include the reference.) — user642796, Jun 09 '15 at 12:04

score 1 · Answer 1 · answered Jun 10 '15 at 02:47

This is a result of my first supervisor Igor Y. Guran. Its proof it rather long and can be found, for instance, in a book “Topological groups and related structures” by his supervisor Alexander V. Arhangel'skii and co-student Mikhail G. Tkachenko (Atlantis Press, Paris; World Sci. Publ., NJ, 2008), where this results is formulated as Theorem 3.4.23.

A topological group is embeddble in a product of a family of second-countable topological groups if and only if it is $\omega$-narrow

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