I am faced with the very annoying problem of finding a continuous map which will transform the unit square in to the triangle. This is a problem in topology and the map need to obey certain identifications. I am very, very stuck as to how to approach this correctly....
These are the identifications I need.... $$ (0,0) \to (1,0,0)$$ $$ (0,1) \to (1,0,0)$$ $$ (1,0) \to (0,0,1)$$ $$ (1,1) \to (0,0,1)$$ $$ (\frac{1}{2}, 1) \to (0,1,0)$$
This is just the square for the homotopic paths.
I would also really appreciate an example as to how to approach this type of problem.
Hint: Map the square to the circle and then map the circle to the triangle.