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I'm starting to study triangulations of topological spaces by myself. I find really difficult since I've never seen any formal example of a triangulation in any book! So, I began with the one of the simplest examples, the closed disc:

What I know:

1) The closed disc is homeomorphic to the triangle.

2) The realization of the 2-simplex is a triangle in $\mathbb R^2$

3) The triangulation of topological space is a homeomorphism between this one and a realization

What I did:

I made a homeomorphism between the closed disc and a triangle, and I said this one is a triangulation.

Am I wrong? if yes where did I made mistakes?

Thanks in advance.

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The circle $S^1$ is the 1-dim curve, which is the boundary of the 2-dim disk $D^2$ in $\mathbb{R}^2$. The circle can be realized as the ${\textit boundary}$ of the 2-simplex, which is a union of three 1-simplices (the edges of the triangle). –  Sammy Black Oct 19 '12 at 20:04
@SammyBlack sorry I meant the closed disc –  user42912 Oct 19 '12 at 20:06
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