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I am not getting a fact whether if $X\,\times\,Y$ is homeomorphic to $Y\,\times\,Y$ then is it true that $X$ is homeomorphic to $Y$? Actually I want to know the result for say $X=[0,1]$ and $Y=[0,1)$.

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    You can deduce that the if ... then statement is false from your example. Clearly in that example $X$ isn't homeomorphic to $Y$, so you just have to show that $X \times Y$ is homeomorphic to $Y \times Y$ (which it is).2011-02-12

2 Answers 2