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Could you help me to construct a mapping from a triangle onto a cone?

Let $X$ be a triangle: $\{(x,y): |x| \le y \le 1\}$ with the subspace topology in $\mathbb{R}^2$.

Let $Y$ be a cone: $\{(x_1, x_2, x_3): x_1^2 + x_2^2 = x_3^2 \le 1\}$ with the subspace topology in $\mathbb{R}^3$.

Construct a quotient mapping from $X$ onto this $Y$.

Thank you.

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