Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What is a surjective continuous function from a 3-torus onto a cube? What are some examples and could I see some illustrations? Are they topologically equivalent to a 3-torus obtained by embedding a cube in 3-dimensional space or higher, and physically gluing the three pairs of opposite faces of the cube?

share|improve this question

1 Answer 1

For example (representing the $3$-torus as $0 \le x, y, z \le 1$ with $0$ and $1$ identified), $f(x,y,z) = [4 x(1-x), 4 y(1-y), 4 z(1-z)]$. Note that most points of the cube have $8$ inverse images in the $3$-torus.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.