Under what conditions on topology of a given space $X$ it can be written as product space $Y\times Y$ for some other topological space $Y$. Lets call such space $Y$ a square root of X. Then given that square root of $X$ exists is it unique (within topological isomorphism) ?
For which topological spaces $X$ can one write $X \approx Y \times Y$? Is $Y$ unique?
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general-topology
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7http://mathoverflow.net/questions/60395/square-roots-of-mathbb-r2n is relevant. – 2012-07-10
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4http://math.stackexchange.com/questions/78055/decomposition-of-a-manifold también. – 2012-07-10