I'm having trouble showing that the Klein bottle defined as a quotient space of $I^2$ with relation $(x,-1)R(x,1)$ and $(-1,y)R(1,-y)$ is Hausdorff and that it can be expressed as $X\cup Y$ where $X,Y$ are homeomorphic to the Möbius strip and $X\cap Y$ is homeomorphic to $S^1$.
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1Your description of $R$ seems to be missing a minus sign on one of the $x$'s or on one of the $y$'s. As it stands, the quotient is not a Klein bottle but a torus. – Andreas Blass Apr 10 '13 at 03:13
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ah thank you I forgot to include a minus sign on y – user62931 Apr 10 '13 at 12:07
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2Maybe the picture found here will help you visualize it. – Viktor Vaughn Jun 16 '14 at 00:02
