## Quotient space of the torus with two points identified [closed]

Take the torus $T=S^{1} \times S^{1}$. Choose two points $x, y \in T$ and define a quotient topology by identifying $x$ and $y$. Let $X$ denote the quotient space. Prove that: a) Compute the fundamental group of $X$. b) Prove that $X$ is not homeomorphic to a surface.

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Please don't abuse this website. Go to math.stackexchange.com for help in homework problems. – GH May 3 2011 at 20:36
homework. . – Tilman May 3 2011 at 20:37
See mathoverflow.net/faq#whatnot. – GH May 3 2011 at 20:37