domains Definition and 103 Threads

I'm working on solving coupled PDEs (mass diffusion - heat transfer - continuum mechanics) in problems where the solution domain changes depending on the solution (call it an intrinsic coupling if you will). This happens either due to addition of material to the domain or damage of the domain...

How can companies sell domains names, i mean how do they own it-- is there a way to get them for free. How come we have to pay for them by the year.

I'm lost! My book of topology says that its possible to construct a (continuous!) function f:[0,1] -> R^n such that the image is a ball {x: |x|<=1} I can't imagine how is it any possible to do such things. The book doesn't give any example or prove of it. It's just a comment. Any ideas? I...