4. Let the torus T be the image of the map T(u, v) = (x(u, v), y(u, v), z(u, v)) = ((R+r cos v) cos u, (R+r cos v) sin u, r sin v) for all u, v € [0, 2π]. Here T is neither injective nor surjective and R>r> 0. Show that T is a sequentially compact set in R³.

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Q: f) Every continuous map T² RP2 is homotopic to the constant map.

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