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- Thread starter Amer
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- #1

- Jan 26, 2012

- 37

Define $f : X \times Y \to X \times Z$ by $f \left( \left( x_1, x_2, x_3, ...\right) , y \right) = \left( \left( y, x_4, x_1,x_6,x_3,x_8,x_5,x_{10} ...\right) , x_2 \right)$

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- Feb 7, 2012

- 2,818

That construction actually proves a stronger result, namely:

Define $f : X \times Y \to X \times Z$ by $f \left( \left( x_1, x_2, x_3, ...\right) , y \right) = \left( \left( y, x_4, x_1,x_6,x_3,x_8,x_5,x_{10} ...\right) , x_2 \right)$

Given any two topological spaces $Y$ and $Z$, there exists a space $X$ such that $X\times Y$ is homeomorphic to $X\times Z.$