(no subject)
I haven't heard any topology lectures and am looking at an application where some knowledge would really help. I have a continuous map f from an n-torus T^n to the n-dimensional real space R^n.
What interesting properties of f(T^n) can I expect from continuity to carry into R^n? Is f(T^n) necessarily bounded? It seems like f in my case is not invertible. Is that to expected for any f? Can I calculate the volume of f(T^n) by some sort of integral (symbolically or analytically)? f(T^n) has a boundary B. What's the preimage of this boundary in T^n like?
What interesting properties of f(T^n) can I expect from continuity to carry into R^n? Is f(T^n) necessarily bounded? It seems like f in my case is not invertible. Is that to expected for any f? Can I calculate the volume of f(T^n) by some sort of integral (symbolically or analytically)? f(T^n) has a boundary B. What's the preimage of this boundary in T^n like?